A -10.0 point charge and a +20.0 point charge are 15.0 apart on the x-axis.?

Question

What is the electric potential at the point on the x-axis where the electric field is zero? (V)

What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

(N/C)

Answer 1

Since for a point charge V~q/|r| and E~q/r^2 their null points differ. See the refs.

Assuming your numbers are in units of C and m, and referring to the -10 charge as q1 and the +20 charge as q2, the null-field point is d1 = 36.2132 m and d2 = 51.2132 m, from q1 and q2 respectively.

1. Voltage at E-field null point = k(q1/|d1|+q2/|d2|) = 1028013401.10322 V

2. There are two voltage null points, as the phrasing of the question implies. The "between charges" null point is at 5 m from q1, so d1 = 5 m and d2 = 10 m. At this point E = k(q1/d1^2+q2/d2^2) = -1797510357.47778 N/C