A -3.0 nC charge is on the x-axis at x = -9.0 cm and a +4.0 nC charge is on the x-axis at x = 19 cm. At what point on the y-axis is the electric potential zero?

• A. ±16.7 cm
• B. 0 cm
• C. ±25 cm
• D. ±32 cm

Answer: (A)

Electric potential from point charges simply adds, and it’s a scalar. The total potential at a point is V = k(q1/r1 + q2/r2). Here one charge is negative and the other positive, so their potentials have opposite signs.

Place the point on the y-axis at (0, y). The distances to the charges are r1 = sqrt(0.09^2 + y^2) and r2 = sqrt(0.19^2 + y^2) in meters. The charges are q1 = -3.0 nC and q2 = +4.0 nC. Setting the total potential to zero gives -3.0/r1 + 4.0/r2 = 0, so r2 = (4/3) r1.

Plugging in the distances: sqrt(0.19^2 + y^2) = (4/3) sqrt(0.09^2 + y^2). Squaring and solving yields y^2 = 0.0279 m^2, so y ≈ ±0.167 m, i.e., ±16.7 cm.

Thus the potential is zero at two points on the y-axis, located about 16.7 cm above and below the origin.