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TUTORIAL SHEET ON ELECTROMAGNETICS
Q. 1
Derive the Maxwell’s equations:
i)
Q. 2
ii)
Explain the physical significance of each equation.
Show that the electromagnetic wave equations for the electric field vector and
magnetic field vector in free space are written as
i)
Q. 3.
Q. 4
Q. 5
Q. 6
Q. 7
Q. 8
Q. 9
and ii)
respectively.
If the magnitude of
in a plane wave is 1 amp/meter find the magnitude of
for a plane wave in free space.
Explain the concept of Maxwell’s displacement current and show how it leads to the
modification of Ampere’s circuital law.
Prove that the electromagnetic wave are transverse in nature.
The relative permeability of distilled water is 81. Calculate the refractive index and
velocity of light in it.
If the earth receives 2 cal min – 1 cm -2 solar energy, what are the amplitudes of electric
and magnetic fields of radiation?
Assuming that all the energy from a 1000 watt lamp is radiated uniformly, calculate
average values of intensities of electric and magnetic fields of radiation at a distance of
2 m from the lamp.
Using Maxwell’s relation
and
prove that
is the equation of continuity.
Q. 10 For silver,
and σ = 3 x 10 7 mhos/m, calculate the skin depth at 10 8 Hz
frequency.
Q. 11 If in a time invariant field, the magnetic field associated with a plane
electromagnetic wave has only z – component which is expressed as
then obtain an expression for current density
Q. 12 A plane electromagnetic wave propagating in the x – direction has a wavelength
7.00 mm. The electric field is in the y – direction and its maximum magnitude is
42 V/m. Write suitable equations for the electric and magnetic fields of EM wave.
Q. 13 Show that the Maxwell’s equation in vacuum can be reduced as
, and
Q. 14 Ocean water can be assumed to be non magnetic dielectric with
and σ
= 4.3 mhos/m. (a) Calculate the frequency at which the penetration depth will be 10 cm
and (b) show that for frequencies less than 10 8 Hz , it can be considered as good
conductor.