An electrostatic field $$\overrightarrow {\bf{E}} $$ exists in a given region R. Choose the wrong statement.

A long cylindrical kept along Z-axis carries a current density $${\bf{\hat J}} = {J_0}r{\bf{\hat k}},$$   where $${J_0}$$ is a constant and r is the radial distance from the axis of the cylinder. The magnetic induction $$\overrightarrow {\bf{B}} $$ inside the conductor at a distance d from the axis of the cylinder is

A uniform surface current is flowing in the positive Y-direction over an infinite sheet lying in X-Y plane. The direction of the magnetic field is

The electric field $$\overrightarrow {\bf{E}} \left( {\overrightarrow {\bf{r}} ,\,t} \right)$$  for a circularly polarized electromagnetic wave propagating along the positive Z-direction is

The stateof polarization of light with the electric field vector $$\overrightarrow {\bf{E}} = {\bf{\hat i}}{E_0}\cos \left( {kz - \omega t} \right) - {\bf{\hat j}}{E_0}\cos \left( {kz - \omega t} \right)$$         is

A particle with an initial velocity $${v_0}{\bf{\hat i}}$$ enters a region with an electric field $${E_0}{\bf{\hat j}}$$ and a magnetic field $${B_0}{\bf{\hat j}}.$$ The trajectory of the particle will

A thin conducting wire is bent into a circular loop of radius r and placed in a time dependent magnetic field of magnetic induction.
$$\overrightarrow {\bf{B}} \left( t \right) = {B_0}{e^{ - \alpha t}}{{\bf{\hat e}}_z},\,\,\left( {{B_0} > 0{\text{ and }}\alpha > 0} \right)$$
such that, the plane of the loop is perpendicular to $$\overrightarrow {\bf{B}} \left( t \right).$$ Then the induced emf in the loop is

Which one of the following Maxwell's equations implies the absence of magnetic monopoles?

An infinitely long closely wound solenoid carries a sinusoidally varying current. The induced electric field is

A magnetic dipole of dipole moment $$\overrightarrow {\bf{m}} $$ is placed in a non-uniform magnetic field $$\overrightarrow {\bf{B}} .$$ If the position vector of the dipole is $$\overrightarrow {\bf{r}} ,$$ the torque acting on the dipole about the origin is