E.M. Waves in Free Space, in Dielectrics & in Conductors: Assignment

# E.M. Waves in Free Space, in Dielectrics & in Conductors: Assignment | Electricity & Magnetism - Physics PDF Download

Q.1. A plane electromagnetic wave has the magnetic field given by

where k is the wave number and  are the Cartesian unit vectors in x, y and z directions respectively.
(a) Find the electric field  corresponding to the above wave.
(b) Find the average Poynting vector.

(a)

(b)

Q.2. A plane electromagnetic wave is propagating in a lossless dielectric. The electric field is given by

where c is the speed of light in vacuum, E0, A and k0 are constant and  are unit vectors along the x - and z -axes.
(a) Find the relative dielectric constant of the medium.
(b) Find the constant A.

(a)

Comparing with term

Since

(b)
Since

Q.3. The electric and magnetic fields in the charge free region z > 0 are given by

where ω, k1 and k2 are positive constants. Find the intensity of the wave.

Q.4. (a) A material has conductivity of 10-2 mho / m and relative permittivity of 4. Find the frequency at which the conduction current in the medium is equal to the displacement current.

(b) A uniform plane wave of frequency 10 kHz is propagating in a medium having

σ 10-3S/m, ε = 80ε0 and μ = μ0 . Find the skin depth.

(a)

(b)

Q.5. Write down the electric and magnetic fields for a plane monochromatic wave of amplitude E0 , frequency ω and phase angle zero that is traveling in the direction from the origin to the point (1, 2,1) with polarization parallel to yz plane.

Q.6. A current I is created by a narrow beam of protons moving in vacuum with constant velocity Find the magnitude and direction of the Poynting vector  outside the beam at a radial distance r (much larger than the width of the beam) from the axis.

Let charge per unit length be λ , hence I = λu in z -direction.
The magnetic field at a distance r is
The electric field at a distance r is
Hence Poynting vector

Q.7. An electromagnetically-shielded room is designed so that at a frequency ω = 107 rad/s the intensity of the external radiation that penetrates the room is 1% of the incident radiation. If  is the conductivity of the shielding material, find its minimum thickness.

(a)

(b)

Q.8. (a) A Plan electromagnetic wave is travelling along the positive z -direction. The maximum electric field along the x - direction is 100V/m. Find the maximum values of the power per unit area and the magnetic induction B.
(b) The intensity of a laser in free space is 150mW/m2. Find the corresponding amplitude of the electric field of the laser.
(c) A monochromatic plane wave in free space with electric field amplitude of 1 V/m is normally incident on a fully reflecting mirror. Find the pressure exerted on the mirror.

(a)

(b)

(c)

Q.9. (a) At equilibrium, there cannot be any free charge inside a metal. However, if you forcibly put charge in the interior then it takes some finite time to ‘disappear’ i.e. move to the surface. If the conductivity σ of a metal is 106( Ωm)-1 and the permittivity ε=8.85x10-12 Farad/m, find this time.
(b) A uniform volume charge density is placed inside a conductor (with resistivity 10-2m (Ωm). After what time the charge density becomes 1/(2.718) of its original value.

(a)

(b)

Q.10. An electromagnetic wave is travelling in free space (of permittivity ε0 ) with electric field  Find the average power (per unit area) crossing planes parallel to 4x + 3y= 0.

The document E.M. Waves in Free Space, in Dielectrics & in Conductors: Assignment | Electricity & Magnetism - Physics is a part of the Physics Course Electricity & Magnetism.
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## FAQs on E.M. Waves in Free Space, in Dielectrics & in Conductors: Assignment - Electricity & Magnetism - Physics

 1. What are electromagnetic waves?
Ans. Electromagnetic waves are a form of energy propagation through space or a medium, consisting of electric and magnetic fields oscillating at right angles to each other. They include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
 2. How do electromagnetic waves behave in free space?
Ans. Electromagnetic waves in free space propagate without any medium and travel at the speed of light. They follow the laws of physics, such as the inverse square law, which states that the intensity of the wave decreases with the square of the distance from the source.
 3. What happens to electromagnetic waves when they enter a dielectric material?
Ans. When electromagnetic waves enter a dielectric material, they interact with the atoms and molecules of the material. This interaction causes the waves to slow down and change direction according to Snell's law. The dielectric material can also affect the polarization and absorption of the waves.
 4. How do electromagnetic waves behave inside a conductor?
Ans. Inside a conductor, electromagnetic waves are heavily absorbed due to the high conductivity of the material. The waves induce currents in the conductor, leading to energy dissipation in the form of heat. As a result, electromagnetic waves are rapidly attenuated and do not propagate over long distances in conductors.
 5. How are electromagnetic waves used in practical applications?
Ans. Electromagnetic waves have a wide range of practical applications. They are used in communication systems, such as radio and television broadcasting, satellite communication, and wireless networks. They are also utilized in medical imaging (X-rays and MRI), remote sensing (radar), heating (microwave ovens), and many other areas of technology and science.

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