A charged cork ball of mass m is suspended on a light sting in the presence of a uniform electric field as shown in fig. When `E=(A hat i+B hat j)NC^(-1)`, Where A and B positive numbers, the ball is in equilibirum at `theta`. Find (a) the charge on the ball and (b) the tension in the string.

Answer

(a)`(mg tan theta)/(A+B tan theta)`, (b) `(A mg sec theta)/(A+B tan theta)`

Explanation

`T cos theta+qB=mg`
or `T cos theta=mg-qB`…(i)

`T sin theta=qA` …(ii)
Dividing Eqs.(i) and (ii) we get
`tan theta =(qA)/(mg-qB)`
(a) `q=(mg tan theta)/(A+B tan theta)`
(b) Putting the value of q in Eq. (ii)
`T=(A mg sec theta)/(A+B tan theta)`.