JEE MAIN - Physics (2022 - 26th July Evening Shift - No. 6)
The oscillating magnetic field in a plane electromagnetic wave is given by
$$B_{y}=5 \times 10^{-6} \sin 1000 \pi\left(5 x-4 \times 10^{8} t\right) T$$. The amplitude of electric field will be :
$$B_{y}=5 \times 10^{-6} \sin 1000 \pi\left(5 x-4 \times 10^{8} t\right) T$$. The amplitude of electric field will be :
$$15 \times 10^{2} \,\mathrm{Vm}^{-1}$$
$$5 \times 10^{-6} \,\mathrm{Vm}^{-1}$$
$$16 \times 10^{12} \,\mathrm{Vm}^{-1}$$
$$4 \times 10^{2} \,\mathrm{Vm}^{-1}$$
Explanation
In an electromagnetic wave, the magnitude of the electric field (E) and the magnetic field (B) are related by the speed of the wave (v), which can be represented as :
$$E = Bv$$
Here, B is the magnetic field, E is the electric field, and v is the speed of the electromagnetic wave.
In the given problem, the peak value of the magnetic field is given as :
$$B_0 = 5 \times 10^{-6} T$$
The wave speed (v) can be calculated from the given equation for the magnetic field, using the relationship between frequency (f), wave number (k), and speed :
$$v = \frac{\omega}{k} = \frac{1000 \pi \times 4 \times 10^8}{1000 \pi \times 5} = 8 \times 10^7 m/s$$
Substituting these values into the equation for the electric field gives the peak value of the electric field :
$$E_0 = B_0 v = 5 \times 10^{-6} T \times 8 \times 10^7 m/s = 4 \times 10^2 V/m$$
$$E = Bv$$
Here, B is the magnetic field, E is the electric field, and v is the speed of the electromagnetic wave.
In the given problem, the peak value of the magnetic field is given as :
$$B_0 = 5 \times 10^{-6} T$$
The wave speed (v) can be calculated from the given equation for the magnetic field, using the relationship between frequency (f), wave number (k), and speed :
$$v = \frac{\omega}{k} = \frac{1000 \pi \times 4 \times 10^8}{1000 \pi \times 5} = 8 \times 10^7 m/s$$
Substituting these values into the equation for the electric field gives the peak value of the electric field :
$$E_0 = B_0 v = 5 \times 10^{-6} T \times 8 \times 10^7 m/s = 4 \times 10^2 V/m$$
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