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GATE 2020 || Electromagnetic Theory || National Champion Test

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Question 1

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 E = 6ax + 8ay kV/mm. 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

Question 2

An inductor designed with 400 turns coil wound on an iron core of 16 cm2 cross sectional area and with a cut of an air gap length of 1 mm. The coil is connected to a 230 V, 50 Hz ac supply. Neglect coil resistance core loss iron reluctance and leakage inductance.

The current in the inductor is

Question 3

Find ∇xA at [2, -1, 1] if A = x3zi -3x2yzj + 2xy4k?

Question 4

Match the following.
P. Stokes’s Teorem
Q. Gauss’s Theorem
R. Divergence Theorem
S. Cauchy’s Integral Theorem

1)
2)
3)
4)

Question 5

For the field D, determine the value of the integral for the region bounded by x = 0 and 2, y = 0 and 3, z = 0 and 4. Given,

Question 6

calculate the volume charge density at point (3,5,4)mt if the potential field at any point in a space containing a dielectric material of relative permeability 3.2 is given by V= 5xy + 3+5xz
Volts where x, y, z are in meters.

Question 7

A plane wave is incident normally from air onto dielectric. If the electric field of transmitted wave is –4 times the electric field of the reflected wave, the value of εr of dielectric is

Question 8

A parallel plate capacitor has two plates of area 0.08 m2 each, separated by a distance of 0.01 m and surrounded by a dielectric of . If a charge of magnitude 25 µC is placed on each plate, then determine the energy stored in the capacitor.

Question 9

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4Ω, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time and is given by B(t) = 0.25 sin ωt, where ω= 2π × 50 radian/second. The power absorbed (in watt) by the loop from the magnetic field is ______.

Question 10

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is , where K is given by

Question 11

A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300mm and a cross-sectional area of 300 mm2. The inductance of the coil corresponding to a magnetizing current of 3A will be (Given that μ0 = 4π × 10–7 H/m)

Question 12

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 the electric field intensity, E at a distance r (0 < r < R) inside the sphere?
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Nov 8ESE & GATE EE