Question

We have a square where each side is 2cm. At the top-left corner,there is a charge of -3uC. What does the charge need to be at the bottom left corner and the top right corner so that the electric field at the bottom right corner is zero?

Please show all steps.

Thank you in advance.

Answer 1

r = sqrt(2) a = sqrt(2) (0.02) = 0.0283 m

E = electric field by charge at top left corner at point C = k Q/r² = (9 x 10⁹) (3 x 10^-6) /(0.0283)² = 3.4 x 10⁷ N/C

consider the charge at Top right corner , The charge must cancel the component of electric field E toward it to make the net electric field 0 in that direction

hence

E' = electric field by charge "q" = E Sin45 = 3.4 x 10⁷ (0.71)

k q/r² = (9 x 10⁹) q /(0.0283)² = 3.4 x 10⁷ (0.71) = 2.15 x 10^-6

the charge is positive since the it has to produce electric field in opposite direction.

similarly the charge at lower left corner = q = 2.15 x 10^-6