An expression for oscillating electric field in a plane electromagnetic wave is given as E_z = 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)

<p>Given the electric field expression:</p> <p>$E_z = 300 \sin(5\pi \times 10^3 x - 3\pi \times 10^{11} t) \, \text{Vm}^{-1}$</p> <p>The amplitude of the electric field ($E_0$) is $300 \, \text{V/m}$.</p> <p>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:</p> <p>$v = \frac{\text{Coefficient of } t}{\text{Coefficient of } x} = \frac{3\pi \times 10^{11}}{5\pi \times 10^3} = \frac{3}{5} \times 10^8 \, \text{m/s}$</p> <p>The relationship between the electric field amplitude and the magnetic field amplitude in an electromagnetic wave is given by:</p> <p>$B_0 = \frac{E_0}{v}$</p> <p>Substituting the values for $E_0$ and $v$ into this formula:</p> <p>$B_0 = \frac{300}{\frac{3}{5} \times 10^8}$</p> <p>$B_0 = \frac{300 \times 5}{3 \times 10^8}$</p> <p>$B_0 = \frac{1500}{3 \times 10^8}$</p> <p>$B_0 = 5 \times 10^{-6} \, \text{T}$</p> <p>Therefore, the amplitude of the magnetic field ($B_0$) is $5 \times 10^{-6}$ T.</p>