Electromagnetic Waves

JEE Main level, numerical answer, medium

63 of 165

Question 63 of 165

The intensity of the light from a bulb incident on a surface is 0.22Wm−20.22W{m}^{-2}. The amplitude of the magnetic field in this light-wave is _____ ×10−9T\times {10}^{-9}T
(Given : Permittivity of vacuum ϵ0=8.85×10−12C2N−1m−2{ϵ}_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}, speed of light in vacuum c=3×108ms−1c=3\times {10}^{8}{ms}^{-1})

Show answer and solution

Answer: 43

The intensity is defined as energy per unit time per unit area. Therefore, I=dEAdtI=\dfrac{dE}{Adt}.
Energy density is energy per unit volume. Therefore, Ud=dEAdx{U}_{d}=\dfrac{dE}{Adx}.
Dividing IUd=dxdt=c\dfrac{I}{{U}_{d}}=\dfrac{dx}{dt}=c
⇒Ud=Ic=0.223×108=223×10−10Jm−3\Rightarrow {U}_{d}=\dfrac{I}{c}=\dfrac{0.22}{3\times {10}^{8}}=\dfrac{22}{3}\times {10}^{-10}J{m}^{-3}
Magnetic energy density will be half of total energy density, Therefore, Ub=113×10−10Jm−3{U}_{b}=\dfrac{11}{3}\times {10}^{-10}J{m}^{-3}.
Now energy density in magnetic field is given by, Ub=B22μ0{U}_{b}=\dfrac{{B}^{2}}{2{\mu }_{0}}. Therefore,
Brms22μ0=113×10−10Jm−3\dfrac{{B}_{rms}^{2}}{2{\mu }_{0}}=\dfrac{11}{3}\times {10}^{-10}J{m}^{-3} where Brms2=(B02)=B022{B}_{rms}^{2}=\left(\dfrac{{B}_{0}}{\sqrt{2}}\right)=\dfrac{{B}_{0}^{2}}{2}
⇒B024μ0=113×10−10⇒B0=4×(4π×10−7)×113×10−10⇒B0=4.29×10−8T≃43×10−9T\Rightarrow \dfrac{{B}_{0}^{2}}{4{\mu }_{0}}=\dfrac{11}{3}\times {10}^{-10} \Rightarrow {B}_{0}=\sqrt{4\times \left(4\pi \times {10}^{-7}\right)\times \dfrac{11}{3}\times {10}^{-10}} \Rightarrow {B}_{0}=4.29\times {10}^{-8}T≃43\times {10}^{-9}T

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.