Question

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net electric field at the center of the square? (k=1/4πϵ0=8.99×109N⋅m2/C2 )

Express your answer in terms of the variables d, q, and appropriate constants.

Answer 1

E = 2kq /d^2

Step-by-step explanation:

Let d = side of the square

Distance between the center and corner of the square = a

a = √(d^2 + d^2) / 2

a = √2d^2 / 2

a = (√2 * d) /2

a = d /√2

Let the magnitude of an electric field = E

E = kq/a^2

Put a = d/√2

E = kq / (d/√2)^2

E = kq / d^2 / 2

E = 2kq / d^2