If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\right)\widehat{\mathrm z}$$

is the electric field in a source free region, a valid expression for the electrostatic potential is

Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right){\widehat{\mathrm a}}_\mathrm y$$$ where $${\widehat{\mathrm a}}_\mathrm x$$ , $${\widehat{\mathrm a}}_\mathrm y$$ denote unit vectors along x, y directions, respectively. The magnitude of curl of A is ________

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$.

A hole of radius b (b < a) is now drilled along the length of the wire at a distance d from the center of the wire as shown below.

The magnetic field inside the hole is

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$

The magnetic field at a distance r from the center of the wire is proportional to