1. What is the current in a wire of radius R, if the magnitude of the current density is given by = 0 1 − , in which r is the radial distance and 0 is constant 2. A spherical shell with inner radius ra , and outer radius rb is formed from a material of resistivity ρ. It carries current radially with uniform density in all ρ 1 1 a b direction. Show that it resistance is R = 4π (r − r ) 3. Show that, according to the free-electron model of electrical conduction in metals, and classical physics, the resistivity of metals should be proportional to , where is the temperature in Kelvins. 4. A copper wire of cross-sectional area 2.00 × 10−6 m2 , and length 4.00 m has a current of 2.00 A uniformly distributed across that area. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 30 min? (Resistivity of copper 1.69 × 10−8 Ω ∙ m) 5. The current density in a copper wire is uniform and has magnitude 2.00 × 106 A m2 . Taking copper’s molar mass M = 63.5 × 10−3 kg mol and densityd = 8.96 × 103 kg m3 . Find (a) the density of conduction electron (b) the drift speed of electron in copper wire. 6. Assume the conduction electrons in a metal are free to move like the molecules of a gas. (a) Show that the conductivity of a metal is σ = e 2 nτ m where n is numbers of electrons per unit volume, and τ is the mean time between collisions of a electron with the atoms of metal. The electron mass and charge are m and e respectively. (b) According to classical physics , the kinetic energy of an free electron is given by 1 2 3 mveff 2 = 2 kT, where veff is the effective speed of an electron, and T is the temperature of metal (in Kelvin), and k is the Boltzmann constant. Find the mean free path of an conduction election.
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