A line charge is placed parallel to, and a distance R away from, the axis of a conducting cylinder of radius b that is held at fixed voltagesuch that the potential vanishes at infinity. Finda) the magnitude and position of the image charge(s)b) the potential at any point (expressed in polar coordinates with the origin at the axis of the cylinder and the direction from the origin tothe line charge as the x axis)c) the induced surface charge density, and plot it as a function of angle for R/b2 and 4 in units of N2TTBd) the force on the line charge per unit length

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Asked Sep 28, 2019

It's an electromagnetic problem. 3

A line charge is placed parallel to, and a distance R away from, the axis of a conducting cylinder of radius b that is held at fixed voltage
such that the potential vanishes at infinity. Find
a) the magnitude and position of the image charge(s)
b) the potential at any point (expressed in polar coordinates with the origin at the axis of the cylinder and the direction from the origin to
the line charge as the x axis)
c) the induced surface charge density, and plot it as a function of angle for R/b
2 and 4 in units of N2TTB
d) the force on the line charge per unit length
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A line charge is placed parallel to, and a distance R away from, the axis of a conducting cylinder of radius b that is held at fixed voltage such that the potential vanishes at infinity. Find a) the magnitude and position of the image charge(s) b) the potential at any point (expressed in polar coordinates with the origin at the axis of the cylinder and the direction from the origin to the line charge as the x axis) c) the induced surface charge density, and plot it as a function of angle for R/b 2 and 4 in units of N2TTB d) the force on the line charge per unit length

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check_circleExpert Solution
Step 1

a)

Refer the diagram below.

R
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R

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Step 2

Using Gauss law,

Enda = en
AL
E da
E(27rL)
E =
2πε
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Enda = en AL E da E(27rL) E = 2πε

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Step 3

Potential ...

dr
dr
2T6
A is the constant of integration]
-In (r) +A
2TS0
-In(B)
2πε
LetA
-In (B)
-In (r)
+
2πο
2π6ο
B
В*
In
4πεο
II
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dr dr 2T6 A is the constant of integration] -In (r) +A 2TS0 -In(B) 2πε LetA -In (B) -In (r) + 2πο 2π6ο B В* In 4πεο II

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