If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............

[m_p = 1.67 $$\times$$ 10^$$-$$27 kg, e = 1.6 $$\times$$ 10^$$-$$19C, Speed of light = 3 $$\times$$ 10⁸ m/s]

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^$$-$$1 in a uniform horizontal magnetic field of 3.0 $$\times$$ 10^$$-$$2 T. The maximum emf induced the coil will be ................. $$\times$$ 10^$$-$$2 volt (rounded off to the nearest integer)

In the given figure the magnetic flux through the loop increases according to the relation $$\phi$$_B(t) = 10t² + 20t, where $$\phi$$_B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$$\Omega$$ resistor at t = 5 s is ___________ mA.

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.