First slide

Nature of electromagnetic wave

Question

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{rms} = 6 {Vm}^{- 1}$ . The peak value of the magnetic field is

Moderate

A

$2.83 \times 10^{- 8} T$
B

$0.70 \times 10^{- 8} T$
C

$4.23 \times 10^{- 8} T$
D

$1.41 \times 10^{- 8} T$

Solution

$Given: E_{rms} = 6 {Vm}^{- 1}$
$\frac{E_{rms}}{B_{rms}} = c or B_{rms} = \frac{E_{rms}}{c}$
$B_{rms} = \frac{6}{3 \times 10^{8}} = 2 \times 10^{- 8} T$
$Since, B_{rms} = \frac{B_{o}}{\sqrt{2}}$
$where B_{o} is the peak value of magnetic field.$
$∴ B_{o} = B_{rms} \sqrt{2} = 2 \times 10^{- 8} \times \sqrt{2} T$
$B_{o} \approx 2.83 \times 10^{- 8} T$

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