A point charge Q is moving in a circular orbit of radius R in the xy-plane with an angular velocity $$\omega$$. This can be considered as equivalent to a loop carrying a steady current $${{Q\omega } \over {2\pi }}$$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $$\gamma$$.

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

A loop carrying current $$l$$ lies in the xy-plane as shown in the figure. The unit vector $$\widehat k$$ is coming out of the plane of the paper. The magnetic moment of the current loop is

An infinite long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, $$\left| {\overrightarrow B } \right|$$ as a function of the radial distance r from the axis is best represented by

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N $$ \approx $$ 4 $$ \times $$ 10²⁷ m^-3. Taking $${{\varepsilon _0}}$$ = 10^{- 11} and m $$ \approx $$ 10^{- 30}, where these quantities are in proper SI units.