A +3.0 nC charge is at x=0 cm and a -1.0 nC charge is at x=4 cm. At what point or points on the x-axis is the electric potential zero?

Answer 1

Wherever 3/|x| - 1/|4-x| = 0 , the electric potential is zero.

|x| is the distance from the +3 nC charge and |4-x| is the distance from the -1 nC charge.

To omit the absolute value | | signs and solve algebraically, you need to write and solve separate equations for x<0, 0<x<4 and x>4

For 0<x<4,
3/x - 1/(4-x) = 0
3/x = 1/(4-x)
12 - 3x = x
x = 3

See if there are solutions in the other regions.