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Question

A 3.0nC charge is at x=0 and a -1.0nc chrage is at x=4cm. At what point or points on the x-axis is the electric potential zero?

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Answer 1

Let the elctric potential be zero at a distance d from origin.

=> k*3.0/d - k*1.0/ld-4l = 0

=> 3/d = 1/ld-4l

=> 9(d-4)² = d²

=> 8d² - 72d + 144 = 0

=> d² - 9d + 18 = 0

=> (d-3)(d-6) = 0

=> d = 3cm or d = 6 cm from origin.

Answer 2

Electric potential EP is proportional to q/r, where q is charge and r is distance from charge.

Let k = constant of proportionality

Then, EP = kq/r

Let the potential be zero at distance d cm from 3.0 nC charge. This point is at distance 4 - d cm from -1.0 nC charge.

0 = k * 3.0/d - k * 1.0/(4-d)

k * 3.0/d = k * 1.0/(4-d)

Dividing by k,

3/d = 1/(4-d)

3(4-d) = d

12-3d = d

12 = 4d

d = 12/4 = 3

Ans: 3 cm from 3.0 nC charge.

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