# Ch 19 Electric Potential and Electric Field

```Ch 19 Electric Potential and Electric Field
19.1. Electric Potential Energy: Potential Difference
• Define electric potential and electric potential energy.
• Describe the relationship between potential difference and electrical potential energy.
• Explain electron volt and its usage in submicroscopic process.
• Determine electric potential energy given potential difference and amount of charge.
Potential energy. Electric potential. Potential difference and electrical potential energy.
Example 19.1 Calculating energy.
Example 19.2 How many electrons move through a headlight each second?
The electron volt. Energy units. Conservation of energy.
Example 19.3 Electric potential energy converted to kinetic energy.
Because electric forces are conservative, we can define the change in electric potential energy by
, where is the
work done by all electric forces, and apply the principle of conservation of mechanical energy:
, or
. The change in electric potential is the change in potential energy per unit charge:
.
Positive charges accelerate in the direction of decreasing potential, while negative charges accelerate in the direction of
increasing potential. Units: [ ]
A useful unit in atomic physics is the electron-volt (
):
19.2. Electric Potential in a Uniform Electric Field
• Describe the relationship between voltage and electric field.
• Derive an expression for the electric potential and electric field.
• Calculate electric field strength given distance and voltage.
Voltage between points A and B.
Example 19.4 What is the highest voltage possible between two plates?
Example 19.5 Field and force inside an electron gun
Relationship between voltage and electric field.
The component of ⃗ in any direction is the negative of the rate at which the electric potential changes with distance in that
direction. For a uniform field,
and
. Units: [ ]
19.3. Electrical Potential Due to a Point Charge
• Explain point charges and express the equation for electric potential of a point charge.
• Distinguish between electric potential and electric field.
• Determine the electric potential of a point charge given charge and distance.
Electric potential V of a point charge.
Example 19.6 What voltage is produced by a small charge on a metal sphere?
Example 19.7 What is the excess charge on a Van de Graaff generator?
Electric potential for a point charge:
where is chosen to be zero at infinity. Superposition: The total electric
potential due to two or more charges is the sum of the potentials due to the separate charges.
19.4. Equipotential Lines
• Explain equipotential lines and equipotential surfaces.
• Describe the action of grounding an electrical appliance.
• Compare electric field and equipotential lines.
Grounding.
An equipotential is a surface with a constant value of the electric potential. The electric field is always perpendicular to
equipotentials, and points in the direction of decreasing electric potential. No work is done by electric forces when a particle
moves within an equipotential. The surface of an ideal conductor is an equipotential, and the interior of the conductor also
has the same value for the potential. For a sphere of radius
and charge , we have at the surface
and
19.5. Capacitors and Dielectrics
• Describe the action of a capacitor and define capacitance.
• Explain parallel plate capacitors and their capacitances.
• Discuss the process of increasing the capacitance of a dielectric.
• Determine capacitance given charge and voltage.
Capacitor. The amount of charge Q a capacitor can store. Capacitance.
Capacitance of a parallel plate capacitor.
Example 19.8 Capacitance and charge stored in a parallel plate capacitor
Dielectric. Take-home experiment: building a capacitor. Dielectric strength.
Table 19.1 Dielectric constants and dielectric strengths for various materials at
Things great and small – The submicroscopic origin of polarization.
Definition of capacitance :
. Units: [ ]
.
Parallel-Plate Capacitor: If the area of the plates is ,
their separation is , and the charge on each plate is , then the potential is
electric field is
.
, the capacitance is
, and the
Dielectrics. Filling a capacitor with a (non-conducting) dielectric material decreases the electric field and potential difference
between the plates. If the dielectric constant is , then
where and are the values without the
dielectric. It is assumed that the charge remains the same. Capacitance of a Parallel-plate capacitor filled with a dielectric.
Any dielectric will conduct electricity (reach dielectric breakdown) if the electric field exceeds a value
known as the dielectric strength.
19.6. Capacitors in Series and Parallel
• Derive expressions for total capacitance in series and in parallel.
• Identify series and parallel parts in the combination of connection of capacitors.
• Calculate the effective capacitance in series and parallel given individual capacitances.
Total capacitance in series.
Example 19.9 What is the series capacitance?
Total capacitance in parallel.
Example 19.10 A mixture of series and parallel capacitance.
Capacitors in series. When a potential difference V is applied across several capacitors connected in series, the capacitors
have identical charge Q. The sum of the potential differences across all the capacitors is equal to the applied potential
difference V. Capacitors connected in series can be replaced with an equivalent capacitor that has the same charge Q and the
same total potential difference V as the actual series capacitors. Series combination:
Capacitors in parallel. When a potential difference V is applied across several capacitors connected in parallel, that potential
difference V is applied across each capacitor. The total charge Q stored on the capacitors is the sum of the charges stored on
all the capacitors. Capacitors connected in parallel can be replaced with an equivalent capacitor that has the same total
charge Q and the same potential difference V as the actual capacitors. Parallel combination:
19.7. Energy Stored in Capacitors
• List some uses of capacitors.
• Express in equation form the energy stored in a capacitor.
• Explain the function of a defibrillator
Example 19.11 Capacitance in a heart defibrillator.
The potential energy of a charged capacitor may be viewed as being stored in the electric field between its plates:
( )
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Glossary / Section Summary / Conceptual Questions / Problems and Exercises
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