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April 2007
Electromagnetism I
Assignment (Due Date: 16th April 2007)
(1) A long cylinder carries a charge density ρ = kr 2 where r is distance from the axis. Find
E inside the cylinder.
(2) A point charge of mass m is dropped from a distance D from an infinite grounded conducting
plane. How long will it take for the charge to reach the plane?
(3) A phonograph record carries a uniform surface charge density σ. If it rotates at an angular
velocity ω what is the current density K at a distance r from the center?
−
→
−
→
→
(4) If B is uniform show that A = 21 −
r × B.
(5) Show that the magnetic field of a dipole can be written as:
−
→
B =
µ0
→
→
(3(−
m · r̂)r̂ − −
m)
4πr 3
−
→
−
→
→
(6) Show that Lorentz force law viz., F = q(−
v × B ) results from a Lagrangian
L =
2
1 −̇
−
→
→
r · A)
r − q(−̇
m→
2