Electromagnetic Waves

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, r = 9, has the electric field, Ex = E0 (kz - 2 106t) Vm-1 where E0 is the amplitude and k is the wave vector. Among the following options, the incorrect choice is

1. The direction of propagation of the electromagnetic wave is along +z
2. The speed of the electromagnetic wave inside the medium is 108 ms-1
3. The wavelength of the electromagnetic wave inside the medium is 300 m
4. The magnetic field is given by the relation By = E0v (kz - 2 106t) where v is the speed of the electromagnetic wave inside the medium

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:

1. Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
2. Zero between the plates and non-zero outside
3. Zero at all places
4. Constant between the plates and zero outside the plates

The electric field in a plane electromagnetic wave is given by Ez = 60 (5x + 1.5 109 t) V/m Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

1. Bz = 60 (5x + 1.5 109 t) T
2. By = 60 (5x + 1.5 109 t) T
3. By = 2 10-7 (5x + 1.5 109 t) T
4. Bx = 2 10-7 (5x + 1.5 109 t) T

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:

1. There is no current
2. Displacement current of magnitude equal to I flows in the same direction as I
3. Displacement current of magnitude equal to I flows in a direction opposite to that of I
4. Displacement current of magnitude greater than I flows but can be in any direction

The property which is not of an electromagnetic wave travelling in free space is that:

1. They are transverse in nature
2. The energy density in electric field is equal to energy density in magnetic field
3. They travel with a speed equal to 1 0 0
4. They originate from charges moving with uniform speed

The electromagnetic radiation which has the smallest wavelength are

1. X-rays
2. Gamma rays
3. Ultraviolet rays
4. Microwaves

If the ratio of relative permeability and relative permittivity of a uniform medium is 1 : 4. The ratio of the magnitudes of electric field intensity (E) to the magnetic field intensity (H) of an EM wave propagating in that medium is (Given that 0 0 = 120 ):

1. 30 : 1
2. 1 : 120
3. 60 : 1
4. 120 : 1

In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of 2.0 1010 Hz and amplitude 48 V m-1. Then the amplitude of oscillating magnetic field is : (Speed of light in free space = 3 108 m s-1)

1. 1.6 10-8 T
2. 1.6 10-7 T
3. 1.6 10-6 T
4. 1.6 10-9 T

The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is

1. 36 107 J
2. 36 104 J
3. 36 105 J
4. 1 105 J

When light propagates through a material medium of relative permittivity r and relative permeability r, the velocity of light, v is given by (c-velocity of light in vacuum)

1. v = c
2. v = r r
3. v = r r
4. v = c r r

The magnetic field of a plane electromagnetic wave is given by B = 3 10-8 (1.6 103 x + 48 1010 t) j, then the associated electric field will be :

1. 9 (1.6 103 x + 48 1010 t) k V/m
2. 3 10-8 (1.6 103 x + 48 1010 t) i V/m
3. 3 10-8 (1.6 103 x + 48 1010 t) i V/m
4. 9 (1.6 103 x - 48 1010 t) k V/m

The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability 0 and permittivity 0 is (Given that c - velocity of light in free space)

1. 0 0c
2. c
3. 1c
4. c 0 0

A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by V = V0 t The displacement current between the plates of the capacitor, would then be given by :

1. Id = V0 C t
2. Id = V0 C t
3. Id = V0 C t
4. Id = V0 C t

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

1. - j + k, - j + k
2. j + k, j + k
3. - j + k, - j - k
4. j + k, - j - k

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is : (c = speed of electromagnetic waves)

1. 1 : 1
2. 1 : c
3. 1 : c2
4. c : 1

Light with an average flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence having surface area 20 cm2. The energy received by the surface during time span of 1 minute is :

1. 12 103 J
2. 24 103 J
3. 48 103 J
4. 10 103 J

Which colour of the light has the longest wavelength?

1. blue
2. violet
3. red
4. green

A parallel plate capacitor of capacitance 20 is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :

1. zero, zero
2. zero, 60
3. 60 , 60
4. 60 , zero

An EM wave is propagating in a medium with a velocity v = v i. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along

1. −z direction
2. +z direction
3. −y direction
4. −x direction

In an electromagnetic wave in free space the root mean square value of the electric field is Erms = 6 V m-1. The peak value of the magnetic field is

1. 2.83 10-8 T
2. 0.70 10-8 T
3. 4.23 10-8 T
4. 1.41 10-8 T

Out of the following options which one can be used to produce a propagating electromagnetic wave?

1. A chargeless particle
2. An accelerating charge
3. A charge moving at constant velocity
4. A stationary charge

A 100 resistance and a capacitor of 100 reactance are connected in series across a 220 V source. When the capacitor is 50\% charged, the peak value of the displacement current is

1. 2.2 A
2. 11 A
3. 4.4 A
4. 11 2 A

The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong ?

1. Ultraviolet rays
2. -rays
3. X-rays
4. Infra-red rays

A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C = Velocity of light)

1. 2EC2
2. EC2
3. EC
4. 2EC

Light with an energy flux of 25 104 W m-2 falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm2, the average force exerted on the surface is

1. 1.25 10-6 N
2. 2.50 10-6 N
3. 1.20 10-6 N
4. 3.0 10-6 N

The condition under which a microwave oven heats up a food item containing water molecules most efficiently is

1. Microwaves are heat waves, so always produce heating.
2. Infra-red waves produce heating in a microwave oven.
3. The frequency of the microwaves must match the resonant frequency of the water molecules.
4. The frequency of the microwaves has no relation with natural frequency of water molecules.

An electromagnetic wave of frequency = 3.0 MHz passes from vacuum into a dielectric medium with relative permittivity r = 4.0. Then

1. Wavelength is doubled and frequency becomes half.
2. Wavelength is halved and frequency remains unchanged.
3. Wavelength and frequency both remain unchanged.
4. Wavelength is doubled and frequency unchanged.

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to

1. the speed of light in vacuum
2. reciprocal of speed of light in vacuum
3. the ratio of magnetic permeability to the electric susceptibility of vacuum
4. unity

The electric field associated with an em wave in vacuum is given by E = i 40 (kz - 6 108 t) where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is

1. 2 m-1
2. 0.5 m-1
3. 6 m-1
4. 3 m-1

The electric and the magnetic field, associated with an e.m. wave, propagating along the +z-axis, can be represented by

1. E = E0 i, B = B0 j
2. E = E0 k, B = B0 i
3. E = E0 j, B = B0 i
4. E = E0 j, B = B0 k