Question

two positive charge and two negative charges of magnitude (Q) at the corners of a square of length (L) such that the like charges are at diagonally opposite corners. determine the magnitude and direction of the force on one of the positive charges due to the other three charges

Answer 1

Let +Q be at top right corner and bottom left corner of the square.

Let -Q be at top left corner and bottom right corner of the square.

Length of the side of a square is L.

k = 8.99 * 10⁹ N.m² /C² is the Coulomb's force constant.

Let's calculate the magnitude and direction of the force on the positive charge at the top right corner due to the other three charges.

X component of the magnitude of the force on the positive charge at the top right corner due to the other three charges is,

F_x = k Q² cos 180 / L² + k Q² cos 45 / 2*L² + k Q² cos 270 / L²

F_x = - k Q² / L² + 0.707 k Q² / 2L² + 0

F_x = -0.6465 k Q² / L²

Y component of the magnitude of the force on the positive charge at the top right corner due to the other three charges is,

F_y = k Q² sin 180 / L² + k Q² sin 45 / 2*L² + k Q² sin 270 / L²

F_y = 0 + 0.707 k Q² / 2L² + - k Q² / L²

F_y = -0.6465 k Q² / L²

The magnitude of the force on the positive charge at the top right corner due to the other three charges is,

F = (F_x² + F_y²)^1/2

F = 0.914 k Q² / L²= 8.219 * 10⁹ Q² / L² N

The direction of the force on the positive charge at the top right corner due to the other three charges is,

Theta = tan^-1 (F_y / F_x)

Theta = 225⁰from the +x axis measured in anticlockwise direction.