A 3.7 nC charge is on the xaxis at X1= 7 cm and a 4.2 nC charge is on the xaxis at X2 = 20 cm.
Part A
At what point or points on the y axis is the electric potential zero?
Express your answer using two significant figures. If there is more than one answer, separate them by a comma.
1 Answer

If the potential at (0, u) is 0, so also is the potential at (0, u).
Potential at (0, u) due to the 3.7nC charge is kQ/r where r is the distance between (0, u) and (7, 0).
Here r = √(u² + (7)²) = √(u² + 49)
So this potential is (9.0 x 10⁹ x (3.7) x 10 ⁻⁹)/√(u² + 0.0049)
Similarly the potential due to the 4.2nC charge is
is (9.0 x 10⁹ x 4.2 x 10 ⁻⁹)/√(u² + 0.04)
If the total potential at (0, u) is 0, then
(9.0 x 10⁹ x 3.7 x 10 ⁻⁹)/√(u² + 0.0049) +
9.0 x 10⁹ x 4.2 x 10 ⁻⁹)/√(u² + 0.04), giving
√(u² + 0.0049)/3.7 = √(u² + 0.04)/4.2 →
4.2²(u² + 0.0049) = 3.7²(u² + 0.04) →
u = ±0.34m = ±34cm.
The points on the yaxis of zero potential are
(0, 34), (0, 34).