PYQs Based test 4: Electromagnetic Fields

Two electrodes, whose cross-sectional view is shown in the figure below, are at the same potential.

The maximum electric field will be at the point

A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of . The relative permittivity of the dielectric material is equal to 2. The value of constant ε₀ is 8.85 × 10⁻¹² F/m. The energy stored in the dielectric in Joules is

If the magnetic field intensity (H) in a conducting region is given by the expression,

$\mathrm{H}={\mathrm{x}}^2\hat{\mathrm{i}}+{\mathrm{x}}^2{\mathrm{y}}^2\hat{\mathrm{j}}+{\mathrm{x}}^2{\mathrm{y}}^2{\mathrm{z}}^2\hat{\mathrm{k}}$ A/m. The magnitude of the current density, in A/m², at x = 1 m, y = 2 m, and z = 1 m, is

A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is J = Jₐr³ẑ for the region r < b where r is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for r < b) is

A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity εᵣ₁ = 2. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity εᵣ₂, as shown in Figure (ii), the capacitance is doubled. The value of εᵣ₂ is ______.