# Full Syllabus Set-3

```Code No. 55/1/2
Series : SKS / 1
Candidates must write the Code on
the title page of the answer-book.
R.No.


Please check that this question paper contains 7 printed pages.
Code number given on the right hand side of the question paper should be written on the
title page of the answer-book by the candidate.
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Please check that this question paper contains 26 questions.
Please write down the Serial Number of the question before attempting it.
15 minutes time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only
and will not write any answer on the answer-book during this period.
PHYSICS (Theory)
Time allowed : 3 hours
Maximum Marks : 70
General Instructions
1.
2.
All questions are compulsory. There are 26 questions in all.
This question paper has five sections: Section A, Section B, Section C, Section D and
Section E.
3. Section A contains five questions of one mark each, Section B contains five questions of two
marks each, Section C contains twelve questions of three marks each, Section D contains one
value based question of four marks and Section E contains three questions of five marks
each.
4. There is no overall choice. However, an internal choice has been provided in one question of
two marks, one question of three marks and all the three questions of five marks weightage.
You have to attempt only one of the choices in such questions.
5. You may use the following values of physical constants wherever necessary.
c = 3 × 108 m/s
h = 6.63 × 10–34 Js
e = 1.6 × 10–19 C
µo = 4 ×10–7 T m A–1
–12 2
C N–1 m–2
0 = 8.854 × 10
1
4 0
 9  109 N m2 C–2
me = 9.1  10–31 kg
mass of neutron = 1.675 × 10–27 kg
mass of proton = 1.673 × 10–27 kg
Avogadro Numbers = 6.023 ×1023 per gram mole
Boltzmann constant = 1.38 × 10–23 JK–1
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Section A
( 5×1= 5 Marks)
1) Two charges of magnitudes –2Q and + Q are located at points (a, 0) and (4a, 0) respectively.
What is the electric flux due to these changes through a sphere of radius '3a' with its centre at the
origin?
2) How does the mutual inductance of a pair of coils change when
(i) distance between the coils is increased and
(ii) number of turns in the coils is increased ?
3) The graph shown in the figure represents a plot of current versus voltage for a given
semiconductor. Identify the region, if any, over which the semiconductor has a negative
resistance.
4) Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel
with each other across an external resistance R. What is the current through this resistance ?
5) The motion of copper plate is damped when it is allowed to oscillate between the two poles of a
magnet. What is the cause of this damping ?
Section B
(5×2= 10 Marks)
6) Define the activity of a given radioactive substance. Write its SI unit.
7) Welders wear special goggles or face masks with glass windows to protect their eyes from
electromagnetic radiations. Name the radiations and write the range of their frequency.
8) Write the expression for the de Broglie wavelength associated with a charged particle having
charge 'q' and mass 'm', when it is accelerated by a potential V.
9) Draw typical output characteristics of an n-p-n transistor in CE configuration. Show how these
characteristics can be used to determine output resistance.
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10) A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern is
observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm
from the centre of the screen. Calculate the width of the slit.
Or
Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the
internal resistance of a cell.
Section C
(12×3 = 36 Marks)
11) A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate
capacitor but has the thickness d/2, where d is the separation between the plates. Find out the
expression for its capacitance when the slab is inserted between the plates of the capacitor.
12) Write the order of frequency range and one use of each of the following electromagnetic
i)
Microwave
ii) Ultra violet rays
iii) Infra-red ray
iv) Gamma ray
13) A convex lens of focal length f1 is kept in contact with a concave lens of focal length f2. Find the
focal length of the combination.
14) In the block diagram of a simple modulator for obtaining an AM signal, shown in the figure,
identify the boxes A and B. Write their functions.
15) (a) For a given a.c., i = im sin  t, show that the average power dissipated in a resistor R over a
complete cycle is
1 2
im R .
2
(b) A light bulb is rated at 100 W for a 220 V a.c. supply. Calculate the resistance of the bulb.
16) A rectangular conductor LATNO is placed in a uniform magnetic field of 0.5 T. The field is
directed perpendicular to the plane of the conductor. When the arm MN of length of 20 cm is
moved towards left with a velocity of 10 m s–1, calculate the emf induced in the arm. Given the
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resistance of the arm to be 5 Ω (assuming that other arms are of negligible resistance) find the
value of the current in the arm.
Or
A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane
normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the
place is 0.4 G and the angle of dip is 60°. Calculate the emf induced between the axle and the rim of
the wheel. How will the value of emf be affected if the number of spokes were increased ?
17) Define the current sensitivity of a galvanometer. Write its SI unit. Figure shows two circuits each
having a galvanometer and a battery of 3 V. When the galvanometers in each arrangement do not
show any deflection, obtain the ratio R1/R2.
18) A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD
carrying 5 A is held directly above AB at a height of 1 mm. Find the mass per unit length of the
wire CD so that it remains suspended at its position when left free. Give the direction of the
current flowing in CD with respect to that in AB. [Take the value of g = 10 m / s2]
19) Draw V-I characteristics of a p-n junction diode. Answer the following questions, giving reasons:
a) Why is the current under reverse bias almost independent of the applied potential upto a
critical voltage ?
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b) Why does the reverse current show a sudden increase at the critical voltage ?
Name any semiconductor device which operates under the reverse bias in the breakdown region.
20) Draw a labelled ray diagram of a refracting telescope. Define its magnifying power and write the
expression for it.
Write two important limitations of a refracting telescope over a reflecting type telescope.
21) Write Einstein's photoelectric equation and point out any two characteristic properties of photons
on which this equation is based. Briefly explain the three observed features which can be
explained by this equation.
22) Name the type of waves which are used for line of sight (LOS) communication. What is the range
of their frequencies ?
A transmitting antenna at the top of a tower has a height of 20 m and the height of the receiving
antenna is 45 m. Calculate the maximum distance between them for satisfactory communication in
LOS mode. (Radius of the Earth = 6.4 × 106 m)
Section D
( 1×4 = 4 Marks)
23) One day Chetan's mother developed a severe stomach ache all of a sudden. She was rushed to the
doctor who suggested for an immediate endoscopy test and gave an estimate of expenditure for
the same. Chetan immediately contacted his class teacher and shared the information with her.
The class teacher arranged for the money and rushed to the hospital. On realising that Chetan
belonged to a below average income group family, even the doctor offered concession for the test
fee. The test was conducted successfully. Answer the following questions based on the above
information :
a) Which principle in optics is made use of in endoscopy ?
b) Briefly explain the values reflected in the action taken by the teacher.
c) In what way do you appreciate the response of the doctor on the given situation ?
Section E
(3×5 = 15 Marks)
24) A long straight wire of circular cross section of radius a carries a steady current I. The current is
uniformly distributed across the cross-section. Apply Ampere’s circuital to calculate the magnetic
field at a point in the region for (i) r < a (ii) r = a (iii) r > a.
Also show the variation of magnetic field B with distance r with the help of graph.
Or
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Explain briefly with the help of a labelled diagram, the principle and working of a moving coil
galvanometer. Define the term 'current sensitivity' of a galvanometer. How is it that increasing current
sensitivity may not necessarily increase its voltage sensitivity? Explain.
What is the nature of the magnetic field in a moving-coil galvanometer and why?
25) (a) Define electric dipole moment. Is it a scalar or a vector ? Derive the expression for the electric
field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due
to the dipole is zero.
Or
Using Guass' law deduce the expression for the electric field due to a uniformly charged spheri•
cal conducting shell of radius R at a point (i) outside and (ii) inside the shell.
Plot a graph showing variation of electric field as a function of r > R and r < R (r being the distance
from the centre of the shell)
26) Using Bohr's postulates, derive the expression for the frequency of radiation emitted when
electron in hydrogen atom undergoes transition from higher energy state (quantum number n) to
the lower state, (n f).
When electron in hydrogen atom jumps from energy state ni= 4 to nf= 3, 2, 1, identify the spectral
series to which the emission lines belong.
Or
(a) Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write two
important conclusions that can be drawn regarding the nature of nuclear force.
(b) Use this graph to explain the release of energy in both the processes of nuclear fusion and
fission.
(c) Write the basic nuclear process of neutron undergoing  -decay. Why is the detection of
neutrinos found very difficult ?
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SOLUTIONS
1) Two charges of magnitudes –2Q and + Q are located at points (a, 0) and (4a, 0) respectively.
What is the electric flux due to these changes through a sphere of radius '3a' with its centre
at the origin ?
Ans: Electric flux through a sphere of radius 3a is
2) How does the mutual inductance of a pair of coils change when
(iii) distance between the coils is increased and
(iv) number of turns in the coils is increased ?
Ans: (i) When the distance between the two coils is increased, mutual
inductance of the pair of coils is decreased because now whole
magnetic flux per unit turn of primary coil is not linked with the secondary coil.
(ii) As mutual inductance M =
0 N1 N 2 A
l
, hence, it is clear that on increasing number of turns
N1 and N2 in two coils the mutual inductance will definitely increase.
3) The graph shown in the figure represents a plot of current versus voltage for a given
semiconductor. Identify the region, if any, over which the semiconductor has a negative
resistance.
Ans: In the region BC of plot the semiconductor has a negative resistance. It is because voltage is
increasing here but the current is decreasing, hence R =
V
is negative.
I
4) Two identical cells, each of emf E, having negligible internal resistance, are connected in
parallel with each other across an external resistance R. What is the current through this
resistance ?
Ans: Net emf of parallel combination = 
Current through the resistance R, I =

R
5) The motion of copper plate is damped when it is allowed to oscillate between the two poles
of a magnet. What is the cause of this damping ?
Ans: The cause of damping is setting up of induced eddy currents in copper plate when magnetic flux
linked with it changes on account of its oscillation between the two poles of a magnet.
6) Define the activity of a given radioactive substance. Write its SI unit.
Ans: Rate of decay (R) or the activity of a radioactive sample is defined as the number of
disintegrations taking place per unit time.
SI unit of activity of a given radioactive substance is a becquerel (1 Bq), where 1 Bq =1 disintegration
per second.
7) Welders wear special goggles or face masks with glass windows to protect their eyes from
electromagnetic radiations. Name the radiations and write the range of their frequency.
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Ans: Welders wear special glass goggles or face masks with glass windows to protect their eyes from
large amount of ultraviolet rays produced by welding arcs.
Frequency range of ultraviolet radiation is from 7 x 1014 Hz to 5 x 1017 Hz.
8) Write the expression for the de Broglie wavelength associated with a charged particle
having charge 'q' and mass 'm', when it is accelerated by a potential V.
Ans: de Broglie wavelength  
h
.
2mqV
9) Draw typical output characteristics of an n-p-n transistor in CE configuration. Show how
these characteristics can be used to determine output resistance.
Ans: Typical output characteristics of an n-p-n transistor in CE configuration are shown in the
following figure :
To determine dynamic output resistance of a transistor at a given value of V CE (say 10 V) and IB (say
30μA), we select two points on eitherside of the operating point (say 10 ± 2 V or 12 V and 8 V
respectively). Observe the value of collector currents from the characteristics corresponding to these
voltages.
Then
10) A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern
is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5
mm from the centre of the screen. Calculate the width of the slit.
Ans: It is given here that wavelength of light  = 500 nm = 5 ×10–7 m, Distance of screen from the
slit D = 1 m and distance of first minimum on the screen from the central maxima x1 = 2.5 mm
= 2.5 × 10–3 m
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Or
Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine
the internal resistance of a cell.
Ans: Determination of internal resistance of a cell : The labelled circuit diagram is shown in figure.
Put the plug in key K1 and adjust rheostat Rh so as to allow flow of a constant current I through the
potentiometer wire due to the driver cell.
Slide the pencil jockey and adjust the length on potentiometer wire to l1 such that galvanometer
shows null deflection. Obviously, fall in potential across 11 length is equal to emf s of given cell i.e.,
 = k l1
Now, put plug in key K2 also and insert a suitable resistance R from R.B. Again slide the pencil
jockey and find the length l 2 to obtain null deflection. Now
V = k l2 ...(ii)
Internal resistance of given cell
11) A slab of material of dielectric constant K has the same area as that of the plates of a
parallel plate capacitor but has the thickness d/2, where d is the separation between the
plates. Find out the expression for its capacitance when the slab is inserted between the
plates of the capacitor.
Ans: Let a dielectric slab of thickness t = d/2 is introduced between the plates of a parallel plate
capacitor without touching the plates, the electric field in air E0 
of dielectric the electric field inside the dielectric changes to E =

but on account of polarization
0
E0
.
K
If potential difference between the plates of capacitor be V now, then clearly
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12) Write the order of frequency range and one use of each of the following electromagnetic
i) Microwave
ii) Ultra violet rays
iii) Infra-red ray
iv) Gamma ray
SOL: (i) Microwave : 1×109 to 3×1011 Hz
detecting speed of tennis or cricket ball or of moving Vehicle. (3) microwave ovens (4) in satellite
communications. (5) in analysis of very fine details of atomic & molecular structure.
(ii) Ultra- violet ray :
7.5 x 1014 Hz to 3 x 1017 Hz use: (1) to destroy bacteria & germs in water
purifiers. (2) in sterilizing surgical instruments. (3) in detection of forged documents, Finger prints in
forensic labs. (4) to preserve food stuffs. (5) in burglar alarm (6) in LASIK eye surgery. (7) checking
mineral samples by fluorescence. (8) in study of electrons arrangement in external shells by UV
absorption spectra.
(iii) Infra red
:
3 x 1011 Hz to 4 x 1014 H use (1) treatment of mascular pain. (2)
producing dehydrated fruits. (3) taking photographs in fog, haze etc. (4) in green house effect to keep
plants warm. (5) in reading secret writings on ancient walls. (6) in solar heaters (7) infrared detectors
in earth satellites (8) semiconductor LED emit infrared rays & are Used in remotes of TV, VCR & hifi systems. (9) in checking purity of chemicals & study of molecular structure.
(iv) Gamma ray :
3 x 1020 Hz to 1022 Hz use: (1) in radio therapy. (2) to initiate some nuclear
reactions. (3) to preserve food stuffs for long time. (4) to study structure of atomic nuclei. (5) to
manufacture polyethylene from ethylene.
13) A convex lens of focal length f1 is kept in contact with a concave lens of focal length f2. Find
the focal length of the combination.
Ans: Consider a thin convex lens L1 of focal length f1 in contact with a thin concave lens L2 of focal
length f2 as shown in figure :
Let a point object O be placed at the common principal axis of two lenses, at a distance 'u'. The
convex lens L1, in the absence of concave lens L2, forms a real image of object O at point .I1 at a
distance where
1 1 1
  .
v1 u f1
However, the refracted ray is further deviated on refraction at concave lens and final image, due to
combination of two lenses, is formed at point I at a distance 'v' from the lenses. We can consider that
for concave lens, the point I1 behaves as an object and the image is formed at I. Thus, from lens
formula, we have
1 1
1
 
v v1 f 2
……..(i)
Adding (i) and (ii), we have
If the lens combination is considered as equivalent to a single lens of equivalent focal length 'feq' then
we have
1 1 1
 
v u f eq
….....(iv)
Comparing (iii) and (iv), we get
1
1 1
 
f eq f1 f 2
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As per sign convention followed fi is +ve but f2 is —ve. Hence, we have
14) In the block diagram of a simple modulator for obtaining an AM signal, shown in the figure,
identify the boxes A and B. Write their functions.
Ans: Box A in the block diagram is a "square law device". It is a non-linear device which transforms
the input signal x(t) = Am sin m t + AC C t and produces an output of the form y (t) = B x(t) + C
x2(t), where B and C are two constants.
Box B in the block diagram is a "band pass filter" centred at frequency C It allows frequencies C
and ( C ± m ) only.
15) (a) For a given a.c., i = im sin  t, show that the average power dissipated in a resistor R
over a complete cycle is
1 2
im R .
2
(b) A light bulb is rated at 100 W for a 220 V a.c. supply. Calculate the resistance of the bulb.
Ans: (a) When an alternating voltage V = Vm sin  t is applied across an ideal resistor, the current in
the circuit is given by I = Im sin  t, where
Average power dissipated per complete cycle of a.c. is given by
(b)
V2
R
V 2 220  220
R

 484
P
100
P
16) A rectangular conductor LATNO is placed in a uniform magnetic field of 0.5 T. The field is
directed perpendicular to the plane of the conductor. When the arm MN of length of 20 cm
is moved towards left with a velocity of 10 m s–1, calculate the emf induced in the arm. Given
the resistance of the arm to be 5 Ω (assuming that other arms are of negligible resistance)
find the value of the current in the arm.
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Ans: Here B =.0.5 T, length of moving conductor 1= 20 cm = 0.2 m and speed v = 10 m s–1
Induced emf | e | = B l v = 0.5 ×0.2 × 10 = 1.0 volt
As resistance of rectangular conductor R = 5 Ω
Current I =

R

1.0
 0.2 A
5
Or
A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane
normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at
the place is 0.4 G and the angle of dip is 60°. Calculate the emf induced between the axle and the
rim of the wheel. How will the value of emf be affected if the number of spokes were increased ?
Ans: As per question number of spokes in wheel n = 8, length of each spoke l = 50 cm = 0.50 m.
angular speed  = 120 rpm =
120
rps = 2 rps = 4π rad s–1, earth's magnetic field BE = 0.4 G =
60
4.0×10–5 T and angle of dip δ = 600.
As the wheel is rotated in a plane normal to the horizontal component BH of the earth's magnetic
field, hence emf induced between the axle and the rim of the wheel
The value of emf remains unaffected if the number of spokes were increased because all the spokes
are connected in parallel.
17) Define the current sensitivity of a galvanometer. Write its SI unit. Figure shows two circuits
each having a galvanometer and a battery of 3 V. When the galvanometers in each
arrangement do not show any deflection, obtain the ratio R1/R2.
Ans: Current sensitivity of a galvanometer is defined as the deflection given by galvanometer when a
unit current is passed through it.
SI unit of current sensitivity is "division A–1".
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In circuit number (I) as galvanometer does not give any deflection, hence the bridge is balanced one
and we have
18) A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD
carrying 5 A is held directly above AB at a height of 1 mm. Find the mass per unit length of
the wire CD so that it remains suspended at its position when left free. Give the direction of
the current flowing in CD with respect to that in AB. [Take the value of g = 10 m / s2]
Ans: The wire CD will remain steady above AB at a height of d =1 mm = 10–3 m, if force on it due to
magnetic field produced on account of current flowing in wire AB just balances its weight. As weight
acts vertically downward, magnetic force must act in vertically upward direction and it is possible
when current in wire CD is flowing along a direction opposite to that in AB as shown in figure.
If m be mass of wire CD per unit length, then
19) Draw V-I characteristics of a p-n junction diode. Answer the following questions, giving
reasons :
a) Why is the current under reverse bias almost independent of the applied potential upto
a critical voltage ?
b) Why does the reverse current show a sudden increase at the critical voltage ?
Name any semiconductor device which operates under the reverse bias in the breakdown
region.
Ans: The V-I characteristics of a p-n junction diode in forward bias and reverse bias arrangement are
shown below :
(i) In reverse bias the junction width increases. The higher junction potential restricts the flow of
majority charge carriers. However, such a field favours flow of minority carriers. Thus, reverse bias
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current is due to flow of minority carriers only. Since the number of minority carriers is very small,
the current is small and almost independent of the applied potential upto a critical (before breakdown)
voltage.
(ii) At a critical (breakdown) voltage the reverse bias current shows a sudden increase. Under
high reverse bias, the high junction field may strip an electron from the valence band, which can
tunnel to the n-side through the thin depletion layer. This mechanism of emission of electrons after a
critical applied voltage leads to a high reverse (breakdown) current.
A zener diode operates under the reverse bias in the breakdown region.
20) Draw a labelled ray diagram of a refracting telescope. Define its magnifying power and
write the expression for it.
Write two important limitations of a refracting telescope over a reflecting type telescope.
Ans: A ray diagram showing the image formation in a refracting telescope for normal adjustment is
being shown in figure.
Magnifying power of telescope in normal adjustment is defined as the ratio of angle subtended (β)
by the final image at the eye to the angle (α) subtended by the object at the eye. It is found that
magnifying power is given by :
m
fo
fe
where fo = focal length of objective and fe = focal length of eye piece.
A refractive type astronomical telescope suffers with the following drawbacks as compared to a
reflecting type telescope :
(i) The image formed has both chromatic as well as spherical aberration.
(ii) It is extremely difficult to design and maintain the mechanical support of the telescope.
21) Write Einstein's photoelectric equation and point out any two characteristic properties of
photons on which this equation is based. Briefly explain the three observed features which
can be explained by this equation.
Ans: Einstein's photoelectric equation is :
According to photon nature of radiation, radiation energy is built up of discrete units, the photons.
Each photon has energy E = h , where h is Planck's constant and  the frequency of radiation.
Moreover, one photon may interact only with one electron present in a metal surface.
Einstein's photoelectric equation successfully explains all the laws of photoelectric emission, as given
below :
(i) Since one photon ejects one photoelectron from a metal surface, number of photoelectrons
emitted per second is proportional to the number of incident photons per second i.e., the intensity of
incident light.
(ii) If  <  o, then kinetic energy is negative, which is impossible. Hence, photoelectric emission
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does not take place for the incident radiation below threshold frequency.
(iii) For  > o, the maximum kinetic energy Kmax is proportional to frequency v of incident light.
If on increasing intensity of light more photons fall on metal surface, it may result in ejection of
greater number of electrons but their energy remains unchanged.
(iv) Photoelectric emission is a consequence of elastic collision between the photon and an electron
inside the metal. Thus, absorption of energy by the electron in the metal from the incident photon is a
single event involving transfer of energy at once without any time lag. As a result, photo-emission
takes place instantaneously.
22) Name the type of waves which are used for line of sight (LOS) communication. What is the
range of their frequencies ?
A transmitting antenna at the top of a tower has a height of 20 m and the height of the receiving
antenna is 45 m. Calculate the maximum distance between them for satisfactory communication
in LOS mode. (Radius of the Earth = 6.4 × 106 m)
Ans: For line of sight (LOS) communication "space waves" are used which travel in straight line
from transmitter antenna to receiver antenna through troposphere.
Range of frequencies of space waves used for LOS communication usually varies from about 50 MHz
to few giga hertz.
As per question hT = 20 m, hR = 45 m and R = 6.4 × 106 m
Maximum distance between two antennas for satisfactory communication in LOS mode :
=16+24 = 40km
23) One day Chetan's mother developed a severe stomach ache all of a sudden. She was rushed
to the doctor who suggested for an immediate endoscopy test and gave an estimate of
expenditure for the same. Chetan immediately contacted his class teacher and shared the
information with her. The class teacher arranged for the money and rushed to the hospital.
On realising that Chetan belonged to a below average income group family, even the doctor
offered concession for the test fee. The test was conducted successfully. Answer the following
questions based on the above information :
a) Which principle in optics is made use of in endoscopy ?
b) Briefly explain the values reflected in the action taken by the teacher.
c) In what way do you appreciate the response of the doctor on the given situation ?
Ans: (a) Principle of total internal reflection of light is used in endoscopy.
(b) The teacher has a concern and caring for her student and his family. She gave him moral support
as well as arranged money needed for test of Chetan's mother. She also rushed to hospital and
supervised herself the progress of tests etc.
(c) The doctor played a role of responsible citizen. On realising that Chetan belonged to a low income
group family, he gave concession for test fee without compromising the procedure of test.
24) A long straight wire of circular cross section of radius a carries a steady current I. The
current is uniformly distributed across the cross-section. Apply Ampere’s circuital to
calculate the magnetic field at a point in the region for (i) r < a (ii) r = a (iii) r > a.
Also show the variation of magnetic field B with distance r with the help of graph.
SOL: MAGNETIC FIELD DUE TO CURRENT THROUGH A LONG CYLINDERICAL
WIRE ( THICK WIRE ) :
Consider an infinite long cylinder of radius R with axis XY. Let I be the current passing through the
cylinder. A magnetic field is set up due to current through the cylinder in the form of circular
magnetic lines of force, with their centres lying on the axis of cylinder. These lines of force are
perpendicular to the length of cylinder.
Case I. Point P is lying outside the cylinder. Let r be the perpendicular distance of point P from the
axis of cylinder, where r > R. Let B be the magnetic field induction at P. It is acting tangential to the
magnetic line of force at P directed into the paper
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Case II. Point P is lying inside cylinder. Here r < R. We may have two possibilities.
(i) If the current is only along the surface of cylinder which is so if the conductor is a cylindrical sheet
of metal, then current through the closed path L is zero. Using Ampere circutal law, we have B = 0
(ii) If the current is uniformly distributed throughout the cross-section of the conductor, then the
current through closed path L is given by
The field at the centre (r = 0) of the thick wire (or cylinder) will he zero.
If we plot a graph between magnetic field induction B and distance from the axis of cylinder for a
current flowing through a solid cylinder, we get a curve of the type as shown in Fig.
Or
Explain briefly with the help of a labelled diagram, the principle and working of a moving coil
galvanometer. Define the term 'current sensitivity' of a
galvanometer. How is it that increasing current sensitivity
may not necessarily increase its voltage sensitivity? Explain.
What is the nature of the magnetic field in a movingcoil galvanometer and why?
SOL: MOVING COIL GALVANOMETER
Moving coil galvanometer: It is a device used for the
detection and measurement of small electric currents or
small p.d.’s of the order of mA and mV.
Principle: A current-carrying coil placed in a magnetic field
experiences a torque, the magnitude of which. depends on the
strength of current.
Construction: It consists of a coil having a large number
of turns of insulated copper wire wound on a metallic
frame. The coil is suspended by means of a phosphorbronze strip and is surrounded by a horse-shoe magnet
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NS. A hair spring is attached to lower end of the coil. The other end of the spring is attached
to the scale through a pointer.
The coil is placed symmetrically between the concave poles of a permanent horse-shoe magnet. There
is a cylindrical soft iron core which not only makes the field radial but also increases the strength of
the magnetic field.
Theory and Working: As the field is radial, the plane of the coil always remains parallel to the field
B . When a current flows through the coil, a torque acts on it. It is given by
 = Force  Perpendicular distance = NIbB  a sin 90° = NIB (ab) = NIBA
Here  =90°, because the normal to the plane of coil remains perpendicular to the field B in all
positions ( Magnetic field is radial ) or plane of coil is parallel to the direction of magnetic field.
Due to deflecting torque, the coil rotates and suspension wire gets twisted. A restoring torque
is set up in the suspension fibre. If  is angle through which the coil rotates and k is the
restoring torque per unit angular twist, then restoring torque, τ = k  .
In equilibrium,
Deflecting torque = Restoring torque
 BNA 
BINA = k 
or   
I
 k 
 BNA 
where 
 = Galvanometer constant (Figure of merit)
 k 
I
Thus the deflection produced in the galvanometer coil is proportional to the current flowing through
it.
(i)A uniform magnetic field provides a linear current scale.
(ii)A soft iron core makes the field radial. It also increases the strength of the magnetic field and
hence increases the sensitivity of the galvanometer.
Significance of radial magnetic field :
In a radial field, the plane of the coil remains parallel to the lines of force in all orientations of the coil
and so the magnitude of the deflecting torque remains constant. Hence the deflection of the
galvanometer is directly proportional to the current in its coil.
Figure of merit of a galvanometer: It is defined as the current which produces a deflection of one
scale division in the galvanometer and is given by
I


k
BNA
Example: A galvanometer having 20 divisions on its scale and a resistance of 50 Ω , when
joined in series to a 1.5-V cell through a resistance of 100 Ω gives full-scale deflection. Find
the figure of merit of the galvanometer.
Sol: The current giving full-scale deflection in the galvanometer is given by
Sensitivity : A galvanometer is said to be sensitive if a small current passed through it produces a
sufficiently large deflection. The sensitivity is of two types : current sensitivity and voltage
sensitivity.
The current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer
when a unit current flows through it.
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If a current I produces a deflection  in the galvanometer, then the current sensitivity is

I


, we have
I
BNA
k
The reverse of current sensitivity is known as 'figure of merit' of the galvanometer.
Voltage Sensitivity It is the deflection produced in the galvanometer, when a unit potential
difference is applied across its coil

V


IR

BNA
kR
the sensitivity of a galvanometer can be increased by increasing the values of N, A and B, and
decreasing the value-of k.
However, N and A cannot be increased beyond a limit, otherwise the resistance and also the mass of
the galvanometer coil would increase undesirably. Therefore, B is made as large as possible and k as
small as possible. The magnetic field B is increased by taking a very strong horse-shoe magnet and
placing a soft-iron core within the coil. The core concentrates the lines of force. The torsional constant
k is made small by using a long and fine suspension strip and a thin spiral spring of phospher-bronze
or quartz. The quartz fibres are silvered to make them conducting.
Factors on which the sensitivity of a moving coil galvanometer depends :
1.
Number of turns N in its coil.
2.
Magnetic field B.
3.
Area A of the coil.
4.
Torsion constant k of the spring and suspension wire.
Factors by which the sensitivity of a moving coil galvanometer can be increased :
1.
By increasing the magnetic field B.
2.
By decreasing the value of torsion constant k.
3.
By increasing the number of turns N of the coil.(not preferred )
By increasing the area A of the coil.(not preferred )
(ii)Torque is uniform for all positions of the coil.
(iii)Plane of the coil, is parallel to the direction of magnetic field (normal to the plane of coil remains
perpendicular to the field B ).
25) (a) Define electric dipole moment. Is it a scalar or a vector ? Derive the expression for the
electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the
potential due to the dipole is zero.
Ans: (a) Two equal and opposite charges of + q and – q separated by a small distance '2a' constitute
an electric dipole of dipole moment p = q.2 a. Generally, the distance '2a' between the charges of
dipole is extremely small.
Electric dipole moment p is a vector and its direction is from –ve charge
to +ve charge.
Let us calculate the electrostatic field intensity at a point P on the
equatorial line at a distance 'r' from mid-point O of an electric dipole AB.
Let us resolve E A and E B along and perpendicular to the dipole
axis. We find that components EA sinθ and EB sinθ nullify each other
and hence
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(b) Equipotential surfaces due to an electric dipole are closed loops around the two charges as shown
in figure. Potential due to the dipole is zero at all the points (P1, P2, O, P3, P4 etc.) situated on its
equatorial plane.
Or
Using Guass' law deduce the expression for the electric field due to a uniformly charged spheri•
cal conducting shell of radius R at a point (i) outside and (ii) inside the shell.
Plot a graph showing variation of electric field as a function of r > R and r < R (r being the
distance from the centre of the shell)
Ans: (i) Electric field outside a conducting spherical shell : Consider a
uniformly charged thin spherical shell of radius R and having a charge Q.
To find electric field intensity at a point P outside the shell situated at a
distance r (r > R) from the centre of shell, consider a sphere of radius r as
the Gaussian surface. All points on this surface are equivalent relative to
given charged shell and, thus, electric field E at all points of Gaussian
surface has same magnitude E and E and n are
parallel to each other.
Total electric flux over the Gaussian surface
From the result it is clear that for any point outside the shell, the effect is, as if whole charge Q is
concentrated at the centre of the spherical shell.
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(ii) Electric field inside a conducting spherical shell : Consider a hollow charged conducting
shell of radius R and having charge Q. To find electrical field at a point P inside the shell, consider a
sphere through point P and having centre O, i.e., r = OP (where r < R) as the Gaussian surface.
The electric flux through the Gaussian surface
26) Using Bohr's postulates, derive the expression for the frequency of radiation emitted when
electron in hydrogen atom undergoes transition from higher energy state (quantum number
n) to the lower state, (n f).
When electron in hydrogen atom jumps from energy state ni= 4 to nf= 3, 2, 1, identify the
spectral series to which the emission lines belong.
Ans: Bohr gave following three postulates for hydrogen atom :
1. An electron revolves round the nucleus in certain specified circular orbits in which it does not
radiate energy. The centripetal force required for uniform circular motion in such a stationary orbit is
provided by electrostatic force of attraction. Thus,
2. For an orbit to be stationary (or non-radiating), the angular momentum of the electron must be an
integer multiple of
h
, where h is the Planck's constant. Thus,
2
3. Whenever an electron shifts from one of its specified non-radiating orbit to another such orbit, it
emits/absorbs a photon whose energy is equal to the energy difference between the initial and final
states. Thus,
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If an electron undergoes transition from higher energy state (quantum number n) to the lower state
(nf), then as per equation (iii), we have
When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2 and 1 respectively, the
emission line belongs to Paschen series (4 - 3), Balmer series (4 - 2) and Lyman series (4 -1).
Or
(a) Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write
two important conclusions that can be drawn regarding the nature of nuclear force.
(b) Use this graph to explain the release of energy in both the processes of nuclear fusion and
fission.
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(c) Write the basic nuclear process of neutron undergoing  -decay. Why is the detection of
neutrinos found very difficult ?
Ans: (a) The plot of binding energy per nucleon (BE /A) as a function of mass number (A) is shown
in figure.
Two important conclusions which can be drawn regarding the nature of nuclear force are :
(i) From the constancy of the binding energy per nucleon in the range 30 < A < 170 we conclude
that the nuclear force is short ranged one. A particular nucleon will be under the influence of only
some of the neighbouring nucleons which come within the range of the nuclear force:
(ii) As binding energy is always positive, it suggests that nuclear force is attractive in nature and
much stronger than electrostatic repulsion between the protons.
(b) (i) Binding energy per nucleon for heavier nuclei is comparatively small (for 92 U 238 , it is 7.6
MeV/nucleon) as compared to nuclides having mass numbers in the middle range (about 8.5 MeV/
nucleon). It means that heavier nuclides are less stable and prone to disintegrate via nuclear fission.
As a results, of fission we obtain product nuclei having higher binding energy per nucleon, thereby
releasing a large amount of energy (equal to B.E. of product nuclides minus the B.E. of nucleusundergoing fission). The energy released will be about 235 × (8.5 – 7.6) MeV = 200 MeV.
(ii) Consider fusion of 1 H 2 nuclei into a single 2He4 nucleus as an example. B.E. per nucleon of
2
4
1H is 1.11 MeV but B.E. per nucleon of 2He is 7.07 MeV. Thus, when two deuterium nuclei fuse
into a helium nucleus, an energy of about 23.8 MeV will be released, being the difference between
binding energies of a helium nucleus and that of 2 deuterium nuclei.
(c) Beta-particles (or electrons) as such are not present inside a nucleus. However, at the time of  
decay a neutron decays into a proton, an electron and an antineutrino as per equation :
on
0 n  1 p  1 e   Q
where mass and charge of antineutrino particle is zero. Out of the particles formed, the proton remains
within the nucleus itself but electron along with antineutrino come out of nucleus. It is this electron
which is being emitted as beta-particle.
1
1
0
It is very difficult to detect neutrino ( ) and antineutrino ( ) particles because these are massless and
chargeless.
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