Two infinite plane sheets of charge A and B of positive charge have surface charge densities `Ksigma and sigma`, respectively. A metallic ball of mass m and charge +q is attached to a thread and the thread is tied at point P on sheet A. Initially ball is equilibrium at plate P when sheets are uncharged. Find the correct options (K is a constant.)

Options

A. If `Kgt1, angle theta = tan^(-1)(Ksigmag)/(2epsilon_0mg)`.
B. If Klt1, the ball will not leave its equilibrium.
C. If K = 1, the angle `theta = 45^@`.
D. If Kgt1, the angle `theta = tan^(-1) ((K-1)sigmag)/(2epsilon_0mg)`

Answer

B, D

Explanation

b.,d.
If `Klt1`, force due to charge on plate `B` will be greater than the force due to charge on plate `A`, and so ball will remain in contact with plate `A`. It is alos true for `K=1`.
`T cos theta=mg`
`T sintheta=((K-1)sigmaq)/(2epsilon_(0))`
Dividing equation (i) and (ii), we get
`theta=tan^(-1)[((K-1)sigmaq)/(2epsilon_(0)mg)]` for `Kgt1`