GATE EE : Electromagnetic fields National Champion Test for ESE & GATE EE Exams

Question 1

C₀ is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half ofthe entire gap as shown in figureB. is filled with a dielectric of permittivity ε_r, the expression forthe modified capacitance is

Question 2

A capacitor of 4700 µF is connected in a circuit. Once the capacitor is charged, find the charge on positive plate of capacitor?

Question 3

If

is the electric field intensity,

is equal to

Question 4

Given a vector field F, the divergence theorem states that

Question 5

A parallel plate capacitor is shown in below figure. It is made of two square metal plates of 400 m side. The 14 mm space between the plates is filled with two layers of dielectrics of ε_r = 4, 6 mm thick and ε_r = 2, 8 mm thick. Neglecting fringing of fields at the edges the capacitance is

Question 6

At first the capacitor is connected to 8.0 V battery and afterwards disconnected and then reconnect to 16.0 V battery. What will be the effect of charge on the plate?

Question 7

Two semi-infinite dielectric regions separated by a plane boundary at y = 0. The dielectric constant of region 1(y < 0) and region 2 (y > 0) are 2 and 5, respectively. Region 1 has uniform electric field

, where

and

are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is

Question 8

The inductance of a long solenoid of length 1000 mm wound uniformly with 30 turns on a cylindrical paper tube of 60 mm diameter is

Question 9

A spherical shell with positive charge moves from point A to point B as shown. What will be the change in differential electric flux dФE through surface element dS?

Question 10

A ball of radius R as 50cm has total charge of 36 mC that is uniformly distributed throughout its volume. What will be the magnitude of electric field at 0 cm?

Question 11

In the circuit shown in the following figure, the switch is closed at time t = 0. The steady state value of the voltage V_c is
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Question 12

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 13

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of αL is obtained by interconnecting these coils, the minimum value of α is ____________.

Question 14

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 15

What will be the expression of reluctance in circular magnetic circuit of length as 2πr with N number of turns, having cross sectional area A, when magnetic flux is flowing around it?

Question 16

The hysteresis loop of a magnetic material has an area of 5 cm² with the scales given as 1 cm = 2 AT and 1 cm = 50 mWb. At 50 Hz, the total hysteresis loss is

Question 17

Two magnetic poles revolve around a stationary armature carrying two coils (c₁– c₁′, c₂ – c₂′) as shown in the following figure. Consider the instant when the poles are in a position as shown. Identify the correct statement regarding the polarity of the induced emf at this instant in coil sides c₁ and c₂

Question 18

An inductor of 0.3125 H, is in steady state condition & carries a current of 2.28 Amp in their circuitry, then how much amount of Magnetic Energy stored in the inductor

Question 19

Two conductors are carrying forward and return current of +I and –I as shown in Fig. The magnetic field intensity

at point P is

Question 20

If an ac voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of

Question 21

Voltage phasors at the two terminals of a transmission line of length 70 km have a magnitude of 1.0 per unit but are 180 degrees out of phase. Assuming that the maximum load current in the line is 1/5^th of minimum 3-phase fault current, which one of the following transmission line protection schemes will NOT pick up for this condition?

Question 22

A lossless transmission line having Surge Impedance Loading (SIL) of 2280 MW is provided with a uniformly distributed series capacitive compensation of 30%. Then, SIL of the compensated transmission line will be

Question 23

A parallel plate capacitor has an electrode area of 100 mm², with a spacing of 0.1mm between the electrodes. The dielectric between the plates is air with a permittivity of 8.85×10^–12 F/m. The charge on the capacitor is 100 V. the stored energy in the capacitor is

Question 24

A capacitor consists of two metal plates each 500 × 500 mm² and spaced 6mm apart. The space between the metal plates is filled with a glass plate of 4mm thickness and a layer of paper of 2mm thickness. The relative permittivities of the glass and paper are 8 and 2 respectively. Neglecting the fringing effect, the capacitance will be (Given that ε₀ = 8.85 × 10^–12 F/m)

Question 25

The charge distribution in a metal-dielectric-semiconductor specimen is shown in the following figure. The negative charge density decreases linearly in the semiconductor as shown. The electric field distribution is as shown in

Question 26

Given the potential functions in free space to be

the magnitude (in volts/metre) and the direction of the electric field at a point (1, -1, 1), where the dimensions are in the metres, are

Question 27

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?

Question 28

Two point charges Q₁ = 10μC and Q₂ = 20μC are placed at coordinate (1, 1, 0) and (–1, –1, 0) respectively. The total electric flux passing through a plane z = 20 will be

Question 29

Determine the correctness or otherwise of the following Assertion [a] and theReason [r].
Assertion: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the sub-synchronous region.
Reason: The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range.

Question 30

In a circular loop of wire of radius R with current I, what will be the magnetic induction B on the axis of the loop at a distance z from the center of the loop?