A small spherical insulator of mass 6.53 × 10-2 kg and charge +0.600 uC is hung by a thin wire of negligible mass. A charge of -0.900 uC is held 0.150 m away from the sphere and directly to the right of it, so the wire makes an angle with the vertical (see the drawing). Find (a) the angle and (b) the tension in the wire.

Question

A small spherical insulator of mass 6.53 × 10-2 kg and charge +0.600 uC is hung by a thin wire of negligible mass. A charge of -0.900 uC is held 0.150 m away from the sphere and directly to the right of it, so the wire makes an angle  with the vertical (see the drawing). Find (a) the angle and (b) the tension in the wire.

bobpursley · Answer

So I picture this as a suspended charge bob, pushed away from vertical.
Let theta be the angle of the wire with verical.

tanTheta=electricforce/gravity
= (kq1*q2/.15^2 )/.0653*9.8

solve that for tan Theta.
then solve for Theta=arctanTheta
finally, cosTheta=mg/tension
solve that for tension