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PHY 201
Test 2s
UNION COUNTY COLLEGE
104
A semicircular disc of radius “R” carries a charge “Q” distributed nonuniformly over its surface. It
is centered at the origin of the xyz 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 yaxis.
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 yaxis
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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View Full Document 2. Determine the integral for the potential at a point “P” along the xaxis
To find the potential "P we will break the
semicircular disc up into elemental charges
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This note was uploaded on 02/07/2011 for the course PHY 201 taught by Professor Gilbert during the Spring '11 term at Union County.
 Spring '11
 Gilbert
 Charge

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