A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane.

Take $${\varepsilon _0} = 8.85 \times {10^{ - 12}}$$ F/m.

The Z component of the E field at (0, 0, 0.1) is closest to

The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I₀ = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by $${V_0} = {{{V_m}} \over {2\pi }}\left( {3 + \cos \alpha } \right)$$, where $${V_m} = 80\pi $$ volts and $$\alpha $$ is the firing angle. If the power delivered to the lossless battery is 1600 W, $$\alpha $$ in degree is________ (up to 2 decimal places).