Question

A charge of -3.81C is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass (radius = 0.0811 m). The charges on the circle are -3.86C at the position due north and +4.93C at the position due east. What is

(a) the magnitude and (b) direction of the net electrostatic force acting on the charge at the center? Specify the direction as an angle relative to due east

Answer 1

here,

the charge placed at the center , q1 = - 3.81 C

radius , r = 0.0811 m

the charge placed in north direction , q2 = - 3.86 C

the charge placed in East direction , q3 = 4.93 C

the net force on the charge at center , F = K * q1 * q3 /r^2 (i) + K * q1 * q2 /r^2 (-j)

F = 9 * 10^9 * 3.81 /0.0811^2 * (4.93 i - 3.86 j) N

F = (2.57 i - 2.01 j) * 10^13 N

a)

the magnitude of net force , |F| = sqrt(2.57^2 + 2.01^2) * 10^13 N

|F| = 3.26 * 10^13 N

b)

the direction of net force , theta = arctan((-2.10) /2.57) = 39.3 degree West of due East