E&M 1, solutions

Problem 1:  (C)

Gauss' law

E4πr2 = ρ(4πr3/3)/ε0

Problem 2:  (E)

Rules for drawing field lines and equipotential lines

Problem 3:  (E)

Gauss' law, the principle of superposition:

Field due to the sphere at P  Ex = (1(/4πε0))σ4πR2/(2R)2 = σ/(4ε0),   Ey = Ez = 0.
Field due to the plane at P  Ez = σ/(2ε0),  Ey = Ex = 0.
E2 = Ex2 + Ey2.  E = (√5/4) σ/ε0.  

Problem 4:  (E)

The principle of superposition, the electric field and potential of a point charge

Problem 5:  (C)

Motion of charges in a uniform magnetic field

Problem 6:  (A)

Ohms law, V = IR

R =  ρ1L1/A1 +  ρ2L2/A2

Problem 7:  (B)

Ampere's law, the Biot-Savart law

B near the surface is given by Bs = μ0I/(2πr) where r = 10-3 m (from Ampere's law).
B at the center of the ring is given by Bc = μ0I/(2R), where R = 10-1 m
(from the Biot-Savart law, dB(r) = (μ0/4π)[Idl×(r-r')/|r-r'|3]).   Bs/Bc = 100/π.

Problem 8:  (C)

Force between current-carrying wires, right-hand rule

image

Problem 9:  (A)

Faraday's law

emf = ΔΦB/∆t = A ΔB/∆t

Problem 10:  (D)

RC circuits

V = V0[1 - exp(-(t-t0)/(RC))]