Electromagnetic Waves

JEE Main level, single correct, medium

39 of 165

Question 39 of 165

The electric field of an electromagnetic wave in free space is represented as E⃗=E0cos⁡(ωt−kz)i^\vec{E}={E}_{0}\cos (\omega t-kz)\hat{i}. The corresponding magnetic induction vector will be :

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Answer: (B) B⃗=E0Ccos⁡(ωt−kz)j^\vec{B}=\dfrac{{E}_{0}}{C}\cos (\omega t-kz)\hat{j}

Given E⃗=E0cos⁡(ωt−kz)i^\vec{E}={E}_{0}\cos (\omega t-kz)\hat{i}:
Clearly, (ωt−kz)(\omega t-kz) term represents, electromagnetic wave is travelling along +z+z direction or along k^\hat{k}.
Now, in vector form, direction of electromagnetive wave is given by C^=E^×B^\hat{C}=\hat{E}\times \hat{B}. Therefore, magnetic field is along j^\hat{j}.
Also, we know that B0=E0C{B}_{0}=\dfrac{{E}_{0}}{C}, where CC is speed of light.
Therefore, B⃗=E0Ccos⁡(ωt−kz)j^\vec{B}=\dfrac{{E}_{0}}{C}\cos (\omega t-kz)\hat{j}.

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