electric field?

Question

Two electric charges q1= -8.0 (micro) C and q2= +2.0 (micro) C are separated by 2.0 m. Determine the point( other then Infinity) at which the total electric field is zero.

Please show work

Answer 1

Basic formula:
E = 1/(4*pi*epsilon0) * |q|/r^2

You need to find the field for q1 vs. distance, then find the field for q2 vs. distance. When E1 = E2, because the signs of q1 and q2 are opposite, the total field will be 0.

|q1| / r1^2 = |q2| / r2^2 the 4*pi*epsilons cancel out

but r2 = 2meters - r1 when the fields are equal

|q1| / r1^2 = |q2| / (2 - r1)^2

8 / r1^2 = 2 / (4 - 4r1 + r1^2)

Solve for r1. It looks like there are 2 real solutions to the quadratic -- one in between q1 and q2 and one further away from q2.

.