# MCQs on Electromagnetic Theory | Page – 10

1. A solid sphere made of insulating material has a radius R and has a total charge Q distributed uniformly in its volume. What is the magnitude of electric field intensity, E, at a distance r (o<r<R) inside the sphere?

Let we assume a Gaussian surface inside the sphere (x < R) From Gauss’s law
ψ = Q enclosed
$Q_{enclosed}= \frac{Q}{ \frac{4}{3} \pi R^3} \times \frac{4}{3} \pi r^3 = \frac{Qr^3}{R^3}$
Again Qenclosed = surface integral of (D.ds)
$So, \; frac{Qr^3}{R^3} = D \times 4 \pi r^2 = \epsilon_o E \times 4 \pi; r^2$

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

A wave E = 50 sin(108 t – 2z) uy has component of a E in y direction and it travel in z direction. The given wave with +2z shall move in the negative z direction.

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

The polarization vector and direction of travel are perpendicular to each other. So, Dot production of two vector is zero.

4. Which statement is not correct for the transmission line parameter R, L, G and C?

G is not equal to I/R, where G is conductance per unit length of the conductor and is due to the dielectric medium separating the conductor.

5. Skin depth is proportional to

Skin depth is given as
$\delta = \sqrt{ \frac {1}{ \pi f \mu_o \mu_r \sigma}}$
.

6. 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 the radian frequency of E. It is same the radium 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.

7. An ac voltage source v = vo sinω+ is connected across a parallel plate capacitor C. If conductor current & id respectively then which is true among following relation?

The conduction current in the connecting wire
$i_c = c \frac {dv}{dt} = c \omega V_o \cos \omega t$
For Parallel plate capacitor of area A and plate thickness d,
C = ε A/d
Electric field E in the dielectric is E = v/d.
So, D = ε E = ε (Vo/d) sin ωt
Displacement current id
$i_d = \int_{s}{ \frac{ \delta D}{ \delta t} ds} = ( \epsilon \frac{A}{d}) V_o \omega \cos \omega t$
Therefore, ic = id.

8. What is the value of skin depth as 100 Hz in a material having μr = 1.0 and &sigma = 3.60 × 107 s/m?

Skin depth of a material is given as,
$\delta = \sqrt { \frac {1}{ \pi f \mu_o \mu_r \sigma}}$.

9. A plane wave magnetic field is represented by Bx = 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, Ex = Ey = 0 and By = Bz = 0.

10. Which following statement are not true for line parameters R, L, G and C of transmission line?

For each line LC = μ ε G/c = σ/ε.

11. In a lossless medium the intrinsic impedance η 60π and μr = 1. The relative dielectric constant εr shall be

For free space ηo = & radiac; (μ/ε = 12 π for any lossless medium with μr= 1
$\eta = \sqrt{ \frac{ \mu_o \mu_r} { \epsilon_o \epsilon_r}} = 60 \pi$
So ε r = 4.

12. When a lossy capacitor with a dielectric of permittivity ε and conductivity σ operates at a frequency ω the loss tangent for the capacitor is given by

As C = Aε/d
R = d/(σ A)
CR = A ε/d
d/(&sigma A) = ε/σ
tan δ = I R/Ic = V/(R.V&omega c) = I/(ω CR)
So, tan δ = I(ω ε/σ) = σ/(ω ε).

13. The characteristic impedance of a transmission on line is

Characteristic impedance of transmission line is given as,
$z_o = \sqrt { \frac{L}{C}}$
So it is independent of length.

14. For a lossy transmission line, the characteristic impedance does not depend on

A transmission line is said to be lossless if both its conductor and dielectric are lossless or R = O and G = O
So characteristic impedance be,
$z_o = \sqrt{ \frac{ {L}{C} }$
Inductance and capacitance are not depends the load terminating the line.

15. For distortion less line which of following relation are true?

A distortionless line is one in which the attention constant α is frequency independent while the phase constant is linearly dependent on frequency. For this line, the condition applicable is R/L = G/C.

16. If R = 84 ohm/Km, G = 10-6 mho/Km, H = 0.01 H/Km, C = 0.061 μ F/Km and frequency = 1000 Hz, then what is the value of propagation constant of the transmission line?

Z = R + jω L = 84 + j2π 100 × 0.01 = 84 + j 62.83 = 104.9 ∠ 36.8° ohm/Km.
Y = G + jω C = 383.27 × 10-6 ∠ 89.85° mho/Km.
So propagation constant by γ = &radiac; (yz).

17. In frec space E (z,t) = 103 sin(ωt - βz) uy 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 – ux
Now Ey/Hx = ηo = 377 (As free space)
Hx = 103/377 (A/m).

18. For a line characteristic impedance zo terminated is load zo/3, the reflection coefficient is

$Reflection \; co-efficient \; = \frac{Z_L – Z_O}{ Z_L + Z_O}$.

19. The SWR on a lossless transmission line of the characteristic impedance 100 ohm is 3. The line is the terminated by

For a transmission line, reflection co-efficient,
$\Gamma_L = \frac{ Z_L – Z_O}{ Z_L + Z_O} \; and \; SWR = \frac{1 + \Gamma_L}{1 – \Gamma a_L}$
Here ZL = 3 00 ΓL = 200/400 = ½ and SWR = 3.

20. The VSWR of transmission line is

$VSWR = \frac{1 + \Gamma_L}{1 – \Gamma_L} = \frac{Z_L}{Z_O}$.