Electrodynamics (I): Homework 2 Due: October 16, 2014

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Electrodynamics (I): Homework 2
Due: October 16, 2014
Exercises in Griffiths
1.46, 2.6, 2.9, 2.10 (5%, hand-in), 2.15, 2.16, 2.18(5% hand-in), 2.20, 2.21, 2.22, 2.26, 2.33
(5%, hand-in), 2.36, 2.37, 2.39 (5% hand-in), 2.54(35 %, hand-in)
Ex.1 hand-in 10%
The electric field for a static charge distribution is given by
−αr
~ = ke
E
r2
r̂,
(1)
where k and α are positive constants and r̂ is a unit vector along radial direction. Find the
charge density at r and the total charge of this charge distribution.
Ex.2 hand-in
Suppose that the electric field due to a point charge q deviates from the form
r̂
r2
and were
given by
~ =
E
q
r̂
,
4π0 r2+
(2)
where the deviation is very small and satisfies 1.
~ and ∇ × E
~ for r 6= 0. Show that one can still define the electric
(a) 5 % Calculate ∇ · E
potential and find the electric potential φ for a point charge q by setting the potential zero
at r = ∞.
(b) 10% Consider a spherical shell of radius a that carries charge Q. If the charge is
uniformaly distributed in the spherical shell, find the electric potential φ(r) at a distance
r < a from the center of the sphere and reveal the difference due to .
1
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