Question

A small spherical insulator of mass 2.91 × 10^-2 kg and charge +0.600 μC is hung by a thin wire of negligible mass. A charge of -0.900 μC is held 0.150 m away from the sphere and directly to the right of it, so the wire makes an angle θ with the vertical (see the drawing). Find (a) the angle θ and (b) the tension in the wire.

Answer 1

Suppose tension in thread is T and angle with the vertical is theta

Now Using force balance on sphere

In vertical direction

Ty = W

T*cos theta = m*g

In horizontal direction

Tx = Fe

T*sin theta = k*q1*q2/r^2

Now by divinding both equation

T*sin theta/(T*cos theta) = k*q1*q2/(r^2*m*g)

tan theta = k*q1*q2/(r^2*m*g)

theta = arctan (k*q1*q2/(r^2*m*g))

Using givne values:

theta = arctan (9*10^9*0.6*10^-6*0.9*10^-6/(0.150^2*2.91*10^-2*9.81))

theta = 37.1 deg

Part B.

T*cos theta = m*g

T = m*g/(cos theta)

T = 2.91*10^-2*9.81/cos 37.11276 deg

T = 0.358 N

Let me know if you've any query.