Question 89: EM waves

Question

An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$$\pi$$ $$	imes$$ 103x $$-$$ 3$$\pi$$ $$	imes$$ 1011t) Vm$$-$$1
Then, the value of magnetic field amplitude will be :
(Given : speed of light in Vacuum c = 3 $$	imes$$ 108 ms$$-$$1)

Accepted Answer

Given the electric field expression:
$E_z = 300 \sin(5\pi 	imes 10^3 x - 3\pi 	imes 10^{11} t) \, 	ext{Vm}^{-1}$
The amplitude of the electric field ($E_0$) is $300 \, 	ext{V/m}$.
The velocity ($v$) of the wave in the medium is given by the ratio of the coefficients of time and displacement in the wave equation, which can be calculated as:
$v = \frac{	ext{Coefficient of } t}{	ext{Coefficient of } x} = \frac{3\pi 	imes 10^{11}}{5\pi 	imes 10^3} = \frac{3}{5} 	imes 10^8 \, 	ext{m/s}$
The relationship between the electric field amplitude and the magnetic field amplitude in an electromagnetic wave is given by:
$B_0 = \frac{E_0}{v}$
Substituting the values for $E_0$ and $v$ into this formula:
$B_0 = \frac{300}{\frac{3}{5} 	imes 10^8}$
$B_0 = \frac{300 	imes 5}{3 	imes 10^8}$
$B_0 = \frac{1500}{3 	imes 10^8}$
$B_0 = 5 	imes 10^{-6} \, 	ext{T}$
Therefore, the amplitude of the magnetic field ($B_0$) is $5 	imes 10^{-6}$ T.

Answer

1 $$	imes$$ 10$$-$$6 T

Answer

5 $$	imes$$ 10$$-$$6 T

Answer

18 $$	imes$$ 109 T

Answer

21 $$	imes$$ 109 T

EM waves

An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$\pi \times 103x - 3\pi \times 1011t) Vm-1 Then, the value of magnetic field amplitude will be : (Given : speed of light in Vacuum c = 3 \times 108 ms-$1)

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