Question

The amplitude of the electric field in a plane electromagnetic wave is 120 V/m. The amplitude of the magnetic field of the wave is: 
1. 1.2 × 10^-7 T
2. 2.0 × 10-7 T
3. 3.0 × 10⁸ T
4. 4.0 × 10-7 T

Answer 1

Correct Answer - Option 4 : 4.0 × 10-7 T

Concept:

In electromagnetic waves, the ratio of amplitudes of the electric field and the magnetic field is equal to the velocity of the electromagnetic waves in free space.

\(\frac{{{E_0}}}{{{B_0}}} = c\)

\(\frac{{{B_0}}}{{{E_0}}} = \frac{1}{c}\)

Where:

E0 = Electric field

B0 = Magnetic field

c = velocity of light

Calculation:

With E₀ = 120 V/m, the amplitude of the magnetic field of the wave will be:

\(B_0= \frac{E_0}{c}=\frac{120}{3\times 10^8}\)

B₀ = 4.0 × 10-7 T

Derivation:

The intrinsic impedance of the wave is defined as the ratio of the electric field and the magnetic field phasor (complex amplitude), i.e.

\(\frac{{\left| E \right|}}{{\left| H \right|}} = \eta = \sqrt {\frac{\mu }{\epsilon}} \)

Since B = μ H

\(H = \frac{B}{\mu }\)

\(\frac{{\left| E \right|}}{{\left| B \right|}}\mu = \sqrt {\frac{\mu }{\epsilon}}\)

\(\frac{{\left| E \right|}}{{\left| B \right|}} = \sqrt {\frac{1}{{\mu\epsilon }}}\)

\(c = \frac{1}{{\sqrt {{\mu _0}{\epsilon_o}} }},\;\frac{{\left| E \right|}}{{\left| B \right|}} = c\)