A circular conducting coil of radius 1 m is being heated by the change of magnetic field $$\overrightarrow B $$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 $$\mu$$$$\Omega$$. The magnetic field is slowly switched off such that its magnitude changes in time as

$$B = {4 \over \pi } \times {10^{ - 3}}T\left( {1 - {t \over {100}}} \right)$$

The energy dissipated by the coil before the magnetic field is switched off completely is E = ___________ mJ.

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ____________ rad/s when k = 20 N/m.

The value of aluminium susceptibility is 2.2 $$\times$$ 10^$$-$$5. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $${x \over {{{10}^4}}}$$. Then the value of x is _________________.

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x < < 1 m). The particle executes SHM. Its angular frequency of oscillation will be ____________ $$\times$$ 10⁵ rad/s if q² = 10 C².