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 $$ \times $$ 10^{27} m^{-3}. Taking $${{\varepsilon _0}}$$ = 10^{- 11} and m $$ \approx $$ 10^{- 30}, where these quantities are in proper SI units.

A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the xy-plane and a steady current I flows through the wire. The z-component of the magnetic field at the centre of the spiral is