1.

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.)

Answer»

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

Solution :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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