Question
just c please. work for a and b are provided if it helps.

Transcribed Image Text:6. Consider a finite line charge with uniform charge density A and length L:
L
a) Using the following expression for electric potential
V =
In (1+z) = 2
X
dq
1
4πεο r
find the electric potential a distance x to the right of the line charge at the point P.
b) Show that if x >> L your answer to part a) looks like the electric potential of a point charge. The following might be
helpful:
-
●P
1
1
·2² +
2! 3!
2³
+..
for -1 << 1.
c) Now suppose L = 0.08 m and a point charge q = 30 µC is initially 0.03 m to the right of the line charge. If q is moved
0.02 m farther to the right and the change in its potential energy is +46.41 J what is the charge per unit length and total
charge of the line charge?
![so
xd8
dV= Into (L-√+x)
so
V=
V=
V=
L
Št into
A dr
4G (L-r+x)
(2)
(-x) ln | 2+x-2)
ство
V=-_^ In
акво
ㅗ
AKE * {lax - In L+x}]
V=
X
ство
(b) for x>>2
x
Ltk
V = ARE ==/2
але х
so, L looks like
=
L
+
^ In (1+1/2)
ство
en (1+2=/=/=)
Q
а ток
It is very small so
en ( 1 += =/=/2) = = =/=/²2 - 12/17 (1/2) 2²+... ~ / / 2
← Answer to a)
• LA=Q
Q.ED
a point charge Q.](https://content.bartleby.com/qna-images/question/5c07aab6-53ae-4bda-bd88-033e72af521a/0a4eda2f-1bd5-47bb-8c24-0f6a9d6cdaf4/uqn2din_thumbnail.png)
Transcribed Image Text:so
xd8
dV= Into (L-√+x)
so
V=
V=
V=
L
Št into
A dr
4G (L-r+x)
(2)
(-x) ln | 2+x-2)
ство
V=-_^ In
акво
ㅗ
AKE * {lax - In L+x}]
V=
X
ство
(b) for x>>2
x
Ltk
V = ARE ==/2
але х
so, L looks like
=
L
+
^ In (1+1/2)
ство
en (1+2=/=/=)
Q
а ток
It is very small so
en ( 1 += =/=/2) = = =/=/²2 - 12/17 (1/2) 2²+... ~ / / 2
← Answer to a)
• LA=Q
Q.ED
a point charge Q.
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