# Electromagnetic Fields (Test 3)

## Gate Exam : Ee Electrical Engineering

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Q.1
Consider a closed surface S surrounding volume V. If is the position vector of a point inside S, with the unit normal on S, the value of the integral is
A. 3V
B. 5V
C. 10V
D. 15V
Explaination / Solution:

From Divergence theorem, we have The position vector Here, , thus Workspace
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Q.2
A current sheet lies on the dielectric interface x = 0 between two dielectric media with εr1 = 5, μr1 = 1 in Region -1 (x < 0) and εr2 = 5,  μr2 = 2 in Region -2(x > 0) . If the magnetic field in Region-1 at x = 0- is the magnetic field in Region-2 at x = 0+ is A. B. C. D. Explaination / Solution:

From boundary condition Then from Boundary condition Comparing we get A = 30 and B =- 10 Workspace
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Q.3
A dielectric slab with 500mm x 500mm cross-section is 0.4m 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
A. 8.85 × 10-11
B. 8.85 × 10-5
C. 88.5
D. 885
Explaination / Solution:
No Explaination.

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Q.4
The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in W/m2) is
A. 1/30π
B. 1/60π
C. 1/120π
D. 1/240π
Explaination / Solution:

Intrinsic impedance of EM wave Time average power density Workspace
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Q.5
The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogeneous medium of relative permittivity εr and relative permeability  Assuming the speed of light in free space to be 3 × 108 m/s, the intrinsic impedance of free space to be 120π, the relative permittivity εr of the medium and the electric field amplitude Ep are
A. ε= 3, Ep= 120π
B. ε= 3, Ep= 360π
C. ε= 9, Ep= 360π
D. ε= 9, Ep= 120π
Explaination / Solution:

From the expressions of we can write, Workspace
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Q.6
Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y - z plane and parallel to the y axis. The other wire is in the x - y plane and parallel to the x - axis. Which components of the resultingmagnetic field are non-zero at the origin ? A. x,y,z components
B. x,y components
C. y, z components
D. x,z components
Explaination / Solution:

Due to 1 A current wire in x - y plane, magnetic field be at origin will be in x direction.
Due to 1 A current wire in y - z plane, magnetic field be at origin will be in z direction.
Thus x and z component is non-zero at origin.

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Q.7
If a vector field is related to another vector field through which of the following is true? (Note : C and SC refer to any closed contour and any surface whose boundary is C . )
A. B. C. D. Explaination / Solution:

Hence (B) is correct option. Workspace
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Q.8
A plane wave having the electric field components V/m and traveling in free space is incident normally on a lossless medium with which occupies the region y  0. The reflected magnetic field component is given by
A. B. C. D. Explaination / Solution:

In the given problem Reflection coefficient negative So magnetic field component does not change its direction Direction of incident magnetic field So, reflection magnetic field component  Workspace
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Q.9
The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T = 300 K electronic charge = 1.6 × 10-19 C, thermal voltage = 26 mV and electron mobility = 1350 cm2 / V-s The magnitude of the electric field at x = 0.5 μm is
A. 1 kV/cm
B. 5 kV/cm
C. 10 kV/cm
D. 26 kV/cm
Explaination / Solution:
No Explaination.

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Q.10
The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T = 300 K electronic charge = 1.6 × 10-19 C, thermal voltage = 26 mV and electron mobility = 1350 cm2 / V-s The magnitude of the electron of the electron drift current density at x = 0.5 μm is
A. 2. 16 × 104 A/cm2
B. 1.08 × 104 A/cm2
C. 4.32 × 103 A/cm2
D. 6.48 × 102 A/cm2 