GATE EE 2021 : Electromagnetic theory Quiz 7

A vector field is given as:

Then the value of K for which given field is solenoidal

The point form of the relation connecting vector magnetic potential A and current density J is

In a region, current density is

The total current crossing the plane Z = 0, r = 1 in  direction is

A point charge of 5μC is located at origin and another point charge of –5μC is a located at (1, 1, 1). The potential at (0, 1, 0) is

In a non-magnetic medium, the peak value of electric field is given as 24 V/m. If the relative permittivity is given as ε_r = then the time average power per m² is?