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"GATE NATIONAL CHAMPION QUIZ "

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Question 1

A conducting sphere of radius 10 cm is centred at the origin and embedded in a dielectric material with ϵ = 2.5 ϵ_o. If the sphere carries a surface charge of 4 nc/m² then the electric field at

at point (–3 cm , 4 cm, 12 cm) will be

Question 2

Suppose we have a radiating field given by:

A/m, and it is in free space.

Now, determine the value of magnetic flux (in weber) that crosses the surface which is defined in the area given by: 0 and 0.

Question 3

The values of a, b, c such that the vector field

is a irrotational

Question 4

Consider the transmission line circuit:

A 10 V DC source with an internal resistance of 25Ω is connected to a transmission line of length ℓ having an impedance of 100Ω by a switch. The transmission line is terminated with a 900 Ω load resistor.

At which end the third reflection occur and what is the total voltage at that end after the third reflection.

Question 5

A magnetic field in air is measured to be

What current distribution leads to this field? [Hint: The algebra is trivial in cylindrical coordinates]

Question 6

An electric flux density vector is given by The volume charge density ρ_v(C/m³) is given by

Question 7

In a rectangular waveguide for which a= 1.5cm, b=0.8cm,

and

The cut-off frequency and phase constant, respectively are,

Question 8

A parallel plate capacitor with plate area of

and plate separation of

has a voltage

applied to its plates. The displacement current assuming

is?

Question 9

In the transmission line shown, the impedance Z_in (in ohms) between node A and the ground is _________.

Question 10

Calculate the skin depth and wave velocity at 2MHz in aluminium with conductivity 40MS/m and μ_r=1.

Question 11

If directive gain of a half wave dipole is 2.64 W/W, and ohmic losses is 8Ω, then determine its power gain(in dB).

Question 12

A fixed radar station transmits 100 kW at 3 GHz. The smallest ocean-going ship has a radar cross-section of 200 m². The radar antenna gain is 16 dB . If detection requires a minimum of 1 nW/m² at the radar antenna, the effective range of the radar is nearly

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ESE & GATE EC General

Dec 8ESE & GATE EC