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Two infinite plane sheets of charge A an...

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.)

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)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
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`
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