   Chapter 7.R, Problem 80E

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# The magnitude of the repulsive force between two point charges with the same sign, one of size 1 and the other of size q, is F = q 4 π ε 0 r 2 dwhere r is the distance between the charges and ε 0 is a constant. The potential V at a point P due to the charge q is defined to be the work expended in bringing a unit charge to P from infinity along the straight line that joins q and P. Find a formula for V.

To determine

To find:

The formula of the potential V.

Explanation

Given:

Force F=q4πε0r2

One charge is 1, and another charge is q, both of the same sign. Both are point charges.

Formulae used:

The work done formula

Consider F=q4πε0r2

Suppose q is moved from infinity to R.

The force is repulsive therefore, work done:

W=RFdr=limxRxq4πε0r2dr note that we have changed the order limits

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