A plane EM wave of frequency 30 MHz travels in free space along the X -direction. The electric f

step 1 Hello students in this question we have a plane electromagnetic wave EM wave having frequency eq

A plane EM wave of frequency 30 MHz travels in free space...

A plane EM wave of frequency $30 \mathrm{MHz}$ travels in free space along the $X$ -direction. The electric field component of the wave at a particular point of space and time $E=6 \mathrm{~V} / \mathrm{m}$ along $Y$ -direction. Its magnetic field component $\mathrm{B}$ at this point would be: (a) $2 \times 10^{-8} \mathrm{~T}$ along $\mathrm{Z}$ -direction (b) $6 \times 10^{-6} \mathrm{~T}$ along X-direction (c) $6 \times 10^{-8} \mathrm{~T}$ along Y-direction (d) $6 \times 10^{-8} \mathrm{~T}$ along $\mathrm{Z}$ -direction

A plane EM wave of frequency $30 \mathrm{MHz}$ travels in free space along the $X$ -direction. The electric field component of the wave at a particular point of space and time $E=6 \mathrm{~V} / \mathrm{m}$ along $Y$ -direction. Its magnetic field component $\mathrm{B}$ at this point would be:
(a) $2 \times 10^{-8} \mathrm{~T}$ along $\mathrm{Z}$ -direction
(b) $6 \times 10^{-6} \mathrm{~T}$ along X-direction
(c) $6 \times 10^{-8} \mathrm{~T}$ along Y-direction
(d) $6 \times 10^{-8} \mathrm{~T}$ along $\mathrm{Z}$ -direction

Key Concepts

Plane Electromagnetic Waves

Plane electromagnetic waves are solutions to Maxwell's equations where the electric and magnetic fields oscillate sinusoidally and propagate in a specific direction. They have uniform field distributions over planes perpendicular to the propagation direction and are characterized by parameters such as frequency, wavelength, amplitude, and phase.

Relationship Between Electric and Magnetic Fields

In free space, the magnitudes of the electric and magnetic fields in a plane wave are related by the equation E = cB, where c is the speed of light. This relationship is derived from Maxwell's equations and is pivotal in determining one field component when the other is known.

Speed of Light in Free Space

The speed of light in free space, approximately 3 x 10^8 m/s, is a fundamental constant that relates electric and magnetic fields in electromagnetic waves. It is used to derive the relationship E = cB and also determines properties like wavelength when the frequency is known.

Directional Properties of Electromagnetic Waves

Electromagnetic waves propagate with the electric field, magnetic field, and direction of travel being mutually perpendicular. This orthogonality forms a right-handed coordinate system and is essential for ensuring that the fields correctly satisfy the conditions of Maxwell's equations.

Frequency and its Role in Wave Properties

The frequency of an electromagnetic wave determines the rate at which the electric and magnetic fields oscillate and is linked to the wave's energy and wavelength. It is a crucial parameter in describing the temporal behavior of the wave, even though the relationship between E and B (E = cB) is independent of frequency in free space.

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