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.