PHY 201
Test 2s
UNION COUNTY COLLEGE
104
A
semicircular disc of radius “R” carries a charge “Q” distributed
non-uniformly over its surface. It
is centered at the origin of the x-y-z coordinate system shown in the picture.
The disc lies in the y-
x plane
The surface charge density is given by
=a*sin(
), where a is constant with units of
coul/m
2
, and
is measured off the y-axis.
Assume the potential is zero at infinity
1.
Determine the constant “a’ in terms of “Q” and “R”
We are asked to express the constant "a' in terms of "Q" and "R"
I
n our case ;
dq
da
a sin
In the plane of the disk we
chose polar components to
use as our coordiante
system, r =radial distance
fron center and
, the angle
off of the y-axis
Area Element in Polar Coordinates
da
r dr
d
therefor
dq
a sin
r
dr
d
Q
a
d
0
R
0
a sin
d
d
Q
a R
2
a
Q
R
2

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