Question

A positive charge +q₁ is located to the left of a negative charge −q₂. On a line passing through the two charges, there are two places where the total potential is zero. The first place is between the charges and is 3.50 cm to the left of the negative charge. The second place is 7.40 cm to the right of the negative charge.

(a) What is the distance between the charges?
m

(b) Find |q₁|/|q₂|, the ratio of the magnitudes of the charges.

Answer 1

given,

charges q1 and -q2

let the distance between them be x

potential at distance d due to some charge q = kq/d

potential at 3.5 cm to the left of negative charge = 0

k * -q2 / 3.5 + k * q1 / (x - 3.5) = 0

q1 / (x - 3.5) = q2 / 3.5

q1 / q2 = (x - 3.5) / 3.5

potential at 7.4 cm right of the negative charge = 0

k * -q2 / 7.4 + k * q1 / (x + 7.4) = 0

q1 / (x + 7.4) = q2 / 7.4

q1 / q2 = (x + 7.4) / 7.4

(x - 3.5) / 3.5 = (x + 7.4) / 7.4

x = 13.2821 cm

distance between the charges = 13.2821 cm

q1 / q2 = (x - 3.5) / 3.5

q1 / q2 = (13.2821 - 3.5) / 3.5

q1 / q2 = 2.795