JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2022
- Medium
- MCQ
An \(EM\) wave propagating in \(x\)-direction has a wavelength of \(8\,mm\). The electric field vibrating \(y\) direction has maximum magnitude of \(60\,Vm ^{-1}\). Choose the correct equations for electric and magnetic fields if the \(EM\) wave is propagating in vacuum
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(E_{y}=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j }\,Vm ^{-1}\) \(B _{z}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ k }\,T\)
Step-by-step Solution
Detailed explanation
\(B _{0}=\frac{ E _{0}}{ c }=\frac{60}{3 \times 10^{8}}=2 \times 10^{-7}\,T\)
\(\widehat{ E } \times \widehat{ B }\) must be direction of propagation
So, \(\widehat{B} \rightarrow z\)-axis
\(k =\frac{2 \pi}{\lambda}=\frac{\pi}{4} \times 10^{3}\,m ^{-1}\)
\(E _{ y }=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j } Vm ^{-1}\)
\(B _{z}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ k } T\)
More questions from Physics
- Motion of a particle in \(x - y\) plane is described by a set of following equations \(x=4 \sin \left(\frac{\pi}{2}-\omega t\right) m\) and \(y=4 \sin (\omega t) m\). The path of particle will beJEE Mains 2022 Medium
- Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror \((M_1)\) and parallel to the second mirror \((M_2)\) is finally reflected from the second mirror \((M_2)\) parallel to the first mirror \((M_1).\) The angle between the two mirrors will be......\(^o\)JEE Mains 2019 Medium
- Match List\(-I\) with List\(-II:\)
Choose the correct answer from the options given below:List\(-I\) List\(-II\) \((A)\) \(3\) Translational degrees of freedom \((I)\) Monoatomic gases \((B)\) \(3\) Translational,\(2\) rotational degrees of freedoms \((II)\) Polyatomic gases \((C)\) \(3\) Translational,\(2\) rotational and \(1\) vibrational degrees of freedom \((III)\) Rigid diatomic gases \((D)\) \(3\) Translational,\(3\) rotational and more than one vibrational degrees of freedom \((IV)\) Nonrigid diatomic gases JEE Mains 2023 Medium - A particle of mass \(m\) moves on a straight line with its velocity increasing with distance according to the equation \(\mathrm{v}=\alpha \sqrt{\mathrm{x}}\), where \(\alpha\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(\mathrm{x}=0\) to \(\mathrm{x}=\mathrm{d}\), will be _______.JEE Mains 2024 Hard
- Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter \(0.1\, \mu m\). If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that :JEE Mains 2021 Hard
- A Young's doublc\(-\)slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda,\) is \(K\) units. The intensity of light at a point where the path difference is A \(\frac{\lambda}{6}\) is given by \(\frac{n K}{12},\) where \(n\) is an integer. The value of \(n\) is\(......\)JEE Mains 2020 Medium
More PYQs from JEE Mains
- The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda _1/\lambda _2\), of the photons emitted in this process isJEE Mains 2019 Hard
- A tuning fork is vibrating at \(250\, {Hz}\). The length of the shortest closed organ pipe that will resonate with the tuning fork will be ..... \({cm}\) (Take speed of sound in air as \(340\, {ms}^{-1}\) )JEE Mains 2021 Medium