Question

A charge of 4.40 μC is placed at each corner of a square 0.100 m on a side.

   Determine the magnitude of the force on each charge.
   What is the direction of the force on the charge at the upper right corner of the square? Assume that the positive x-axis is directed to the right.

Answer 1

here,

the charge on each corner , q = 4.4 uC

q = 4.4 * 10^-6 C

side of square , a = 0.1 m

the net force on the upper right corner charge , F = K * q^2 /a^2 i + K * q^2 /a^2 j + K * q^2 /(1.41 * a)^2 * ( cos(45) i + sin(45) j)

F = 9 * 10^9 * ( 4.4 * 10^-6)^2 /0.1^2 * ( i + j + (1/2) * ( cos(45) i + sin(45) j) )

F = (5.36 i + 5.36 j) N

the magnitude of force on each charge , |F| = sqrt(5.36^2 + 5.36^2) N = 7.56 N

the direction of force on the upper right corner charge , theta = arctan(5.36/5.36) = 45 degree counterclockwise from +x axis