Electromagnetic Waves

JEE Main level, single correct, medium

30 of 165

Question 30 of 165

A plane EM wave is propagating along xx direction. It has a wavelength of 4 mm4 \mathrm{~mm}. If electric field is in yy direction with the maximum magnitude of 60Vm−160 \mathrm{Vm}^{-1}, the equation for magnetic field is :

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Answer: (A) Bz=2×10−7sin⁡[π2×103(x−3×108t)]k^T\mathrm{B}_z=2 \times 10^{-7} \sin \left[\frac{\pi}{2} \times 10^3\left(x-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}

E=BC⇒60=B×3×108\mathrm{E}=\mathrm{BC} \Rightarrow 60=\mathrm{B} \times 3 \times 10^8
⇒B=2×10−7\Rightarrow \mathrm{B}=2 \times 10^{-7}
Also C=fλ\quad \mathrm{C}=\mathrm{f} \lambda
⇒3×108=f×4×10−3⇒f=34×1011⇒ω=2πf=34×2π×1011⇒ω=π2×103C\begin{aligned} & \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}\end{aligned}
⇒\Rightarrow \quad Electric field ⇒y\Rightarrow y direction
Propagation ⇒x\Rightarrow \mathrm{x} direction
Magnetic field ⇒z\Rightarrow \mathrm{z}-direction

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