- Exam
- JEE Main
- Year
- 2020
- Date
- 9 January
- Shift
- Evening Shift
- Subject
- Physics
- Chapter
- Electromagnetic Waves
JEE Main 2020 · 9 January · Evening Shift · Physics · Electromagnetic Waves
A plane electromagnetic wave is propagating along the direction ^ i...
Options
- A{B}_{0}\dfrac{\overset{^}{i} - \overset{^}{j}}{\sqrt{2}}\cos \left(\omegat - k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)
- B{B}_{0}\dfrac{\overset{^}{j} - \overset{^}{i}}{\sqrt{2}}\cos \left(\omegat + k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)
- C{B}_{0}\overset{^}{k}\cos \left(\omegat - k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)
- D{B}_{0}\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\cos \left(\omegat - k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)
Correct answer
A. {B}_{0}\dfrac{\overset{^}{i} - \overset{^}{j}}{\sqrt{2}}\cos \left(\omegat - k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)
Step-by-step solution
Polarization of EM Wave means Direction of Its electric Field
Electric field vector is along \overset{^}{k}
So, unit electric filed vector, \overset{\to}{E} = \overset{^}{k} (Given)
Direction of wave,\overset{^}{c} = \dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}} (Given)
\overset{^}{B} denotes unit magnetic field vector.
\overset{^}{B} = \overset{^}{C} \times \overset{^}{E}
\overset{^}{B} = \dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}} \times \overset{^}{k} = \dfrac{\overset{^}{i} - \overset{^}{j}}{\sqrt{2}}
General Form is B = ( {B}_{0}\overset{^}{B} ) \cos \left(\omegat - \overset{^}{c}k\right)
where is Magnitude of Magnetic Field
So, B = {B}_{0}\dfrac{\overset{^}{i} - \overset{^}{j}}{\sqrt{2}}\cos \left(\omegat - k\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right)