# The electric field in an electro-magnetic wave (in vacuum) is described by E = Emax sin(Kx - ωt) Where Emax = 100 N/C and K = 1 × 107 m-1, speed of li

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The electric field in an electro-magnetic wave (in vacuum) is described by E = Emax sin(Kx - ωt)

Where

Emax = 100 N/C and K = 1 × 107 m-1, speed of light is 3 × 108 m/s.

What is the amplitude of the corresponding magnetic wave?

1. 4.57 × 10-7 T
2. 2.99 × 10-7 T
3. 3.33 × 10-7 T
4. 2.99 × 107 T

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Correct Answer - Option 3 : 3.33 × 10-7 T

Concept:

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

$η =\frac{E}{H}$

η  = η0 = 120π

Analysis:

E = Emax sin(Kx - ωt)

With Emax = 100 N/C, the magnetic field will be:

With $η =\frac{E}{H}$:

$H =\frac{E}{\eta}$

$H =\frac{100}{120\pi}A/m$

B = μ0 H

$B=4\pi × 10^{-7}× \frac{100}{120\pi }$

B = 3.33 × 10-7 T