Two point charges lie along the y-axis. a charge of q1 = -8.5 μc is at y = 6.0 m, and a charge of q2 = -7 μc is at y = -4.0 m. locate the point (other than infinity) at which the total electric field is zero.

Electric field will be zero at position

Explanation:

Since both charges are of same sign so here net electric field is zero at some location between two charges

So here at the position of net field zero we can say that electric field due to q1 must be counter balanced by field due to q2

Since the distance between two charges here is d = 10 m

now let say the electric field is zero at distance "r" from 8.5 uC charge

so we can say that

now we have

square root both sides

so the position is

double the distance = divide strength by 4

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle