Two charges are fixed in place with a separation d.?

Question

Two charges are fixed in place with a separation d. One charge is positive and has eight times (n = 8) the magnitude of the other charge, which is negative. The positive charge lies to the left of the negative charge, as in the figure. Relative to the negative charge, locate the two spots on the line through the charges where the total potential is zero.

positive distance to the left of -q ___?__ d
positive distance to the right of -q __?___d

Answer 1

One null is at d/9 to left of -q.
Other null is at d/7 to right of -q.
To check, let Q1 = 8, r1 = d, Q2 = -1, r1 = 0, d1,d2=distances of Q1,Q2 to null point, V=voltage at null point.
For 1st null, d1=8d/9, d2=d/9
V = Q1/d1+Q2/d2 = 0
For 2nd null, d1=8d/7, d2=d/7
V = Q1/d1+Q2/d2 = 0