Ncert Exercises & Solutions

A plane EM wave travelling along z-direction is given by $\vec{E} = E_{0} \sin (kz - ωt) \hat{i} and \vec{B} = B_{0} \sin (kz - ωt) \hat{j} . Show that :$

$(i) Evaluate \oint \vec{E} . d \vec{l} over the rectangular loop 1234 shown in figure .$
$(ii) Evaluate \oint \vec{B} . d \vec{s} over the surface bounded loop 1234 .$
$(iii) Use equation \oint \vec{E} . d \vec{l} = - \frac{{dϕ}_{B}}{dt} to prove \frac{E_{o}}{B_{o}} = c .$
$(iv) By using \oint \vec{B} . d \vec{s} = μ_{o} I + ε_{o} \frac{{dϕ}_{E}}{dt}, prove that c = \frac{1}{\sqrt{μ_{o} ε_{o}}} .$

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