Electromagnetic Waves

JEE Main level, single correct, medium

120 of 165

Question 120 of 165

The electric field component of a monochromatic radiation is given by E⃗=2E0cos⁡kzcos⁡ωti^\vec{E}=2{E}_{0}\cos kz\cos \omega t\hat{i}, Its magnetic field B⃗\vec{B} is then given by:

Show answer and solution

Answer: (A) 2E0csin⁡kzsin⁡ωtj^\dfrac{2{E}_{0}}{c}\sin kz\sin \omega t\hat{j}

dEdz=−dBdt\dfrac{dE}{dz}=-\dfrac{dB}{dt}

dEdz=−2E0Ksin⁡⁡kzcos⁡⁡ωt=−dBdt\dfrac{dE}{dz}=-2{E}_{0}K\sin ⁡kz\cos ⁡\omega t=-\dfrac{dB}{dt}

dB=+2E0Ksin⁡⁡kzcos⁡⁡ωtdtdB=+2{E}_{0}K\sin ⁡kz\cos ⁡\omega tdt

B=+2E0Ksin⁡⁡kz∫cos⁡⁡ωtdtB=+2{E}_{0}K\sin ⁡kz\int \cos ⁡\omega tdt

=+2E0kωsin⁡⁡kzsin⁡⁡ωt=+2{E}_{0}\dfrac{k}{\omega }\sin ⁡kz\sin ⁡\omega t

E0B0=ωk=C\dfrac{{E}_{0}}{{B}_{0}}=\dfrac{\omega }{k}=C

B=2E0Csin⁡⁡kzsin⁡⁡ωtB=\dfrac{2{E}_{0}}{C}\sin ⁡kz\sin ⁡\omega t
Propagation of EM radiation, Electric field oscillation and Magnetic field oscillation are perpendicular to each other.
Since propagation of EM radiation is x−x-axis and electric field oscillation is along z−z-axis, the Magnetic field oscillation is along y−y-axis.

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Electromagnetic Waves (Electromagnetic Waves and Maxwell's equations), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.