Problem 6

Two particles having charges of 0.70 nC and 12 nC are separated by a distance of 2 m. At what point along the line connecting the two charges is the net electric field due to the two charges equal to zero?  

Solution

Introduce the distance a from the charge 0.7 nC to the point P, where the net electric field is 0. The net electric field at point P is the sum of two contributions: electric field due to charge 0.7 nC and electric field due to charge 12 nC. They have opposite directions (since both charges are positive). Then the condition that the net electric field is 0 is the following:

where r=2 m is the distance between the charges. From this equation we can find the distance a :