Question

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

Answer 1

 Let q1 = -10.0 nC , and q2 = 20.0 nC 
E1(P) + E2(P) = 0 
|E1| = |E2| 
|q1|/r1^2 = q2/r2^2 
r2/r1 = sqr(q2/|q1|) = sqr 2 
r2 = r1 + d 
Solving : r1 = d/(sqr2 -1) = 33.8 cm ; r2 = 47.8 cm 
(a) V = (1/4pi €o)(q2/r2 + q1/r1) = 110 V 
(b) V=0 |q1|/r1 = q2/r2 
r2 = 2 r1 ; r2 + r1 = d 
solving 
r2 = 28/3 cm ; r1 = 14/3 cm 
E = E1 + E2 = (1/4pi€o)(|q1|/r1^2 + q2/r2^2) 
E is // at X axis and direct from q2 to q1.