A 10 µC charge is at the origin. A -5 µC charge is on the x-axis 10 cm to the right of the origin.

Question

A 10 µC charge is at the origin. A -5 µC charge is on the x-axis 10 cm to the right of the origin. At what point other than at infinity can a 1 µC charge be placed so that there will be no net electrostatic force on it?

Answer 1

The charge of 1 µ C will not experience zero force , when it is in between the two charges as both forces will act in the same direction and so will be added.

To have zero force 1  µ  C charge has to be on the right of - 5  µ  C , say at distance X from it

This 1  µ C will be at a distance of 10 + X from 10  µ C charge

 

The net force on 1  µ C should be zero 

So 

 

K q1 Q/( 10 +X ) ² = K q2 Q / X ²

 

As we have already taken the direction of force , the signs of both q1 and q2 will be taken as positive

5 ( 10+X ) ² = 10 X² 

Solve this equation for the values of X, which is the distance of 1  µ C from - 5  µ C .

Only +ve value of X is to be the answer, -ve is to be ignored