A -3.7 nC charge is on the x-axis at X1= -7 cm and a 4.2 nC charge is on the x-axis 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
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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 y-axis of zero potential are
(0, 34), (0, -34).
