Three charges are at the corners of an isosceles triangle as shown in the figure

Question

Three charges are at the corners of an isosceles triangle as shown in the figure (Figure 1) . The ±5.00?C charges form a dipole.

Part A

Find the magnitude of the force the -10.00?C charge exerts on the dipole.

Part B

Find the direction of the force the -10.00?C charge exerts on the dipole.(Suppose that y-axis directs to the top of the image.)

Part C

For an axis perpendicular to the line connecting the ±5.00?C charges at the midpoint of this line, find the torque (magnitude) exerted on the dipole by the -10.00?C charge.

Part D

Find the direction of the torque.

Explanation / Answer

A)
Let

q1 = +5 micro C

q2 = -5 micro C

Q = -10 micro C

let theta is the angle at upper corner and lower corner.

theta = cos^-1(1.5/2)

= 41.4 degrees

magnitude of force on upper and lower charges exerted by Q,

F1 = F2 = F k*q1*Q/0.02^2

= 9*10^9*5*10^-6*10*10^-6/0.02^2

= 1125 N

Fnet = 2*F*cos(41.4)

= 2*1125*cos(41.4)

= 1687.75 N

B) dowward (-y axis)

C)Torque acting on the dipole, T = F*0.03*sin(41.4)

= 1125*0.03*sin(41.4)

= 22.32 N.m

D) clockwise

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