Electric charge is distributed uniformly along a thin rod of length a , with tot

Question

Electric charge is distributed uniformly along a thin rod of length a, with total charge Q. Take the potential to be zero at infinity. Find the potential at the following points: (the figure (Figure 1) ).

Part A

Find the potential at the point P, a distance x to the right of the rod.

Express your answer in terms of the given quantities and appropriate constants.

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Part B

Find the potential at the point R, a distance y above the right-hand end of the rod.

Express your answer in terms of the given quantities and appropriate constants.

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Part C

In part A, what does your result reduce to as x becomes much larger than a?

Express your answer in terms of the given quantities and appropriate constants.

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Part D

In part B, what does your result reduce to as y becomes much larger than a?

Express your answer in terms of the given quantities and appropriate constants.

Electric charge is distributed uniformly along a thin rod of length a, with total charge Q. Take the potential to be zero at infinity. Find the potential at the following points: (the figure (Figure 1) ).

Part A

Find the potential at the point P, a distance x to the right of the rod.

Express your answer in terms of the given quantities and appropriate constants.

V =

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Part B

Find the potential at the point R, a distance y above the right-hand end of the rod.

Express your answer in terms of the given quantities and appropriate constants.

V =

SubmitMy AnswersGive Up

Part C

In part A, what does your result reduce to as x becomes much larger than a?

Express your answer in terms of the given quantities and appropriate constants.

V =

SubmitMy AnswersGive Up

Part D

In part B, what does your result reduce to as y becomes much larger than a?

Express your answer in terms of the given quantities and appropriate constants.

V =

Explanation / Answer

part a)

V=(kQ/a)ln((x+a)/x)

part b)

dV=kdq/dr

V=kQln((y2+a2)1/2-y)

part c)

x>>>>a

then part a

V=(kQ/a)ln1

V=0

part d)

y>>>>a

V=kQln0=infinite

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