Two positive point charges, each of magnitude q , are fixed on the y -axis at th

Question

Two positive point charges, each of magnitude q, are fixed on the y-axis at the points y=+a and y=a. Take the potential to be zero at an infinite distance from the charges.

Part A

What is the potential V0 at the origin?

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

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Part B

Find the potential at the point (x,0).

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

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Part C

What is the potential when xa?

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

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Part D

Explain why this result is obtained.

Two positive point charges, each of magnitude q, are fixed on the y-axis at the points y=+a and y=a. Take the potential to be zero at an infinite distance from the charges.

Part A

What is the potential V0 at the origin?

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

V0 =

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Part B

Find the potential at the point (x,0).

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

V(x) =

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Part C

What is the potential when xa?

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

V(x) =

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Part D

Explain why this result is obtained.

Explanation / Answer

PART A:

This is particularly easy, since both scalar electric potentials are the same (same q, same r = a, direction doesn’t matter). V0 = V0t + V0b = 2V0t = 2kq /a

PART B:

The x-axis is still symmetric (same distance to each charge), so V = 2Vt, and we can use the Pythagorean theorem for r. V = 2Vt = 2kq /r = (1 /40) (2q/ r)= (1/40) (2q / (a^2 + x^2)

PART C:

As x gets much bigger than a, (a^2 + x^2) x 2 , so V = 2kq /r^2 k.2q/x^2

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