MCQs on Electromagnetic Fields

01․ In a dielectric material an applied field in x direction E_x = 5 v/m gives a polarization of p_x = 3/10π u_x nc/m². The susceptibility of the material is

P = ε_o (ε_{r – 1}) E. Susceptibility = ε_{r – 1} = P/(ε_o. E).

02․ A pure inductor is connected across a voltage source. Find the active power drawn by the inductor?

Active power P = VI cosφ Where V = voltage cross inductor I = current through inductor φ = phase angle between voltage and current When a pure inductor is connected across a voltage source, current lags the voltage by exactly 90°. Therefore, P =VI cos 90 P = 0

03․ In free space E (z, t) = 10³ sin(ωt - βz) u_y v/m. What is the value of H (z, t)

Direction of wave propagation (+z). So E × H must be (+z) direction. Therefore E × H must be – u_x Now E_y /H_x = η_o = 377 (As free space) H_x = 10³/377 (A/m).

04․ In a lossless medium the intrinsic impedance η = 60π and μ_r = 1. The relative dielectric constant ε_r shall be

For free space η_o; {√(μ/ε) = 120π for any lossless medium with μ_r= 1} So, ε_r = 4.

05․ A plane wave magnetic field is represented by B_x = cos(y – ct). The electric and magnetic fields will be zero in the direction

Wave propagating in (+ y) direction. H in (+ x) direction Then E will be in (+ z) direction. So, E_x = E_y = 0 and B_y = B_z = 0.

06․ What is the value of skin depth as 100 Hz in a material having μ_r = 1.0 and & σ = 3.60 × 10⁷ s/m

µ₀ = 4π × 10^-7 Skin depth of a material is given as,

07․ The frequency of the power wave associated with an electromagnetic wave having field as E = e^{-z/δ cos(ω - zδ)} is given by

Here E = e ^{- zδ cos(ω t – z/δ)} Where, ω is frequency in radian of E. It is same the radian frequency of the associated H wave. The frequency of power wave is double the corresponding frequency of E or H wave. Thus the radian frequency of 2ω and cyclic frequency = 2ω/2π = ω / π.

08․ Skin depth is proportional to

Skin depth is given as Where, σ = conductivity in mho/m

09․ A plane wave in a homogeneous medium has E = 50 sin(10⁸t + 2z) u_y V/m. What is the direction of wave propagation

A wave E = 50 sin(10⁸ t – 2z) u_y has vector component of E in y direction and it travels in z direction. The given wave with +2z shall move in the negative z direction. But here it will move in the negative direction.

10․ If n is the polarization vector and k is the direction of propagation plane electromagnetic wave, then

The polarization vector and direction of travel are perpendicular to each other. So, dot product of these two vectors will be zero.