Problem 10: Two point charges of 8µC and -4µC are separated by a distance of 10 cm in the air. At what point on the line joining the two charges is the electric potential zero?

Solution

The point at which the potential is zero is the one on which the potential of the two opposite charges is equal. Suppose this point is at a distance x from 4µC charge. Then it would be at a distance 10-x cm from 8 µC charge. Let V₁ is potential at this point due to charge 8 μC and V₂ is the potential at this point due to charge 4 μC. So

Similarly

According to the condition of the problem,

So the -4 µC charge is at a distance of 3.3 cm from point of zero potential and hence the 8 µC charge will be at a distance of 10 – 3.3 = 6.6 cm from the point.