Question

A -3.1 nC charge is on the x-axis at x1 = -8 cm and a 3.7 nC charge is on the x-axis at x2 = 13 cm .

At what point or points on the y-axis is the electric potential zero?

Answer 1

let A be the position on y axis where net potential is zero. Assume that the point A is at distance y from origin

Potential at point A due to charges of -3.1 nC and 3.7 nC

kq1 / r1 + kq2 / r2 = 0

r1 = sqrt(8^2 + y^2)

r2 = sqrt(13^2 + y^2)

k is the cancle

-(3.1 x 10^-9) / sqrt(8^2 + y^2) + (3.7 x 10^-9) / sqrt(13^2 + y^2) = 0

(3.1 x 10^-9) / sqrt(8^2 + y^2) = (3.7 x 10^-9) / sqrt(13^2 + y^2) = 0

(3.1 x 10^-9) * sqrt(13^2 + y^2) =  (3.7 x 10^-9)*sqrt(8^2 + y^2)

10^-9 is cancled and squaring on both sides

3.1^2*(169 + y^2) = 3.7^2*(64 + y^2)

1624.09 + 9.61*y^2 = 876.16 + 13.69*y^2

748.74 = 4.08*y^2

y = 13.55 m