Electricity and Magnetism I (P331)
Homework 2
Due: Wednesday, September 16, 4:00 PM
1. Find the magnitude of the electric field at a distance
z
above a circular loop of charge
Q
and radius
a
.
Compute the electric field by directly integrating over the charge distribution
1
4
π
0
λ
2
dl
ˆ. (Here, ˆ is
the separation vector, “script
r
” in the text.)
2. The electric field in some region of space is given by
E
=
α
(
r
4

1
r
)ˆ
r
in spherical coordinates.
(a) Find the charge density
ρ
.
(b) Use your answer to (a) to find the total charge contained in a sphere of radius
R
centered at the
origin.
(c) Check your answer to (b) by using the integral form of Gauss’ Law to find the total charge contained
in a sphere of radius
R
centered at the origin.
3. Assume there is a ribbon of electric charge in the
x, y
plane. It extends from

a
≤
y
≤
a
in the
y
direction and infinitely long in the
x
direction. If the surface charge density is
σ
, calculate the electric
field at the position (0
,
0
, d
). (A distance
d
above the origin on the
z
axis.)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 STAFF
 Charge, Magnetism, Work, Electric charge, Fundamental physics concepts, Coaxial cable, charge density

Click to edit the document details