JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2024
- Hard
- MCQ
A plane EM wave is propagating along \(\mathrm{x}\) direction. It has a wavelength of \(4 \mathrm{~mm}\). If electric field is in y direction with the maximum magnitude of \(60 \mathrm{Vm}^{-1}\), the equation for magnetic field is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\mathrm{B}_z=2 \times 10^{-7} \sin \left[\frac{\pi}{2} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{kT}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{E}=\mathrm{BC} \Rightarrow 60=\mathrm{B} \times 3 \times 10^8\)
\(\Rightarrow \mathrm{B}=2 \times 10^{-7}\)
\(\text { Also } \mathrm{C}=\mathrm{f} \lambda\)
\(\Rightarrow 3 \times 10^8=\mathrm{f} \times 4 \times 10^{-3}\)
\(\Rightarrow \mathrm{f}=\frac{3}{4} \times 10^{11}\)
\(\Rightarrow \omega=2 \pi \mathrm{f}=\frac{3}{4} \times 2 \pi \times 10^{11}\)
\(\Rightarrow \omega=\frac{\pi}{2} \times 10^3 \mathrm{C}\)
\(\Rightarrow \quad \text { Electric field } \Rightarrow \mathrm{y} \text { direction }\)
\(\text { Propagation } \Rightarrow \mathrm{x} \text { direction }\)
\(\text { Magnetic field } \Rightarrow z \text {-direction }\)
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