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A charge of -7.00 μC is fixed at the center of a compass. Two additional charges...

A charge of -7.00 μC is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass, which has a radius of 0.200 m. The charges on the circle are -3.00 μC at the position due north and 6.00 μC at the position due east. What are the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east.

Solutions

Expert Solution

Charges

q1 = -7 C (posiioned at centre)

q2 = -3 C (positioned due north)

q3 = 6 C (positioned due east)

radius, r = 0.2 m

Fore on 1 due to 2

F12 = kq1q2/r2

F12 = (9 x109 x 7 x 10-6 x 3 x 10-6)/0.22

F12 = 472.5 N (due south- repulsive)

Force on 1 due to 3

F13 = kq1q2/r (due east - attractive)

F13 = (9 x 109 x 7 x 10-6 x 6 x 10-6)/0.22

F13 = 945 N

magnitude of the effective force

F = (F122 + F132)

F = (472.52 + 9452)

F = 1055.12 N

direction

= tan-1(F12/F13)

= tan-1(-472.5/945)

= tan-1(-1/2)

= -26.56 degrees (due east)

Answer: Magnitude of force, F = 1055.12 N

direction, = -26.56 degrees (due east)

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genius_generous answered 1 year ago

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