Exams › JEE Main › Physics

A plane electromagnetic wave has its electric field oscillating sinusoidally at frequency 2.0*10¹⁰ Hz with amplitude 48 V/m. (a) Find the wavelength of the wave. (b) Find the amplitude of the oscillating magnetic field. (c) Show that the time-averaged energy density of the electric field equals that of the magnetic field. [Take c = 3*10⁸ m/s.]

1. lambda = 1.5 cm, B0 = 1.6*10⁻⁷ T, and u_E(avg) = u_B(avg)
2. lambda = 3.0 cm, B0 = 1.6*10⁻⁷ T, and u_E(avg) = u_B(avg)
3. lambda = 1.5 cm, B0 = 3.2*10⁻⁷ T, and u_E(avg) = u_B(avg)
4. lambda = 0.75 cm, B0 = 1.6*10⁻⁷ T, and u_E(avg) = u_B(avg)

Correct answer: lambda = 1.5 cm, B0 = 1.6*10⁻⁷ T, and u_E(avg) = u_B(avg)

Solution

(a) lambda = c/f = (3*10⁸)/(2*10¹⁰) = 1.5*10⁻² m = 1.5 cm. (b) In an EM wave E0 = c*B0, so B0 = E0/c = 48/(3*10⁸) = 1.6*10⁻⁷ T. (c) Average energy densities: <u_E> = (1/4)*epsilon0*E0² and <u_B> = B0²/(4*mu0). Using B0 = E0/c and c² = 1/(mu0*epsilon0), <u_B> = E0²/(4*mu0*c²) = (1/4)*epsilon0*E0² = <u_E>, proving equality.

Related JEE Main Physics questions

• A plane electromagnetic wave falls on a material surface. If it transfers momentum p and energy E, which statement is true?
• For an electromagnetic wave moving in vacuum, the electric field is expressed as E = E₀ sin(kx − ωt). Which of the following quantities does not depend on the wavelength?
• When an electromagnetic wave enters the ionised region of the ionosphere, the moving electron cloud gives rise to a space current, while the electric field also produces a capacitive displacement current. In this situation, what is the phase relation between the space current and the displacement current?
• The rms electric field associated with sunlight is 720 N/C. What is the mean total energy density of this electromagnetic wave?
• The electric field component of an electromagnetic wave in a medium is given by Eₓ = 0, E_y = 2.5 N/C cos[(2π × 10⁶ rad/m)x - (π × 10⁻² rad/s)t] ŷ, and E_z = 0. The wave is:
• A source of monochromatic green light radiates equally in every direction. If it converts only 3% of the 100 W electrical power it uses into electromagnetic radiation, then the electric-field amplitude of the emitted wave at a point 5 m away from the source is closest to:

⚔️ Practice JEE Main Physics free + battle 1v1 →