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A plane EM wave travelling in vacuum along z-direction is given by $E=E_{0} \sin (k z-\omega t) \hat{i} \text { and } B=B_{0} \sin (k z-\omega t) \hat{j}$a) evaluate $\oint E . d l \quad$ over the rectangular loop 1234 shown in the figureb) evaluate $\int B \cdot d s$ over the surface bounded by loop 1234
A plane EM wave travelling in vacuum along z-direction is given by $E=E_{0} \sin (k z-\omega t) \hat{i} \text { and } B=B_{0} \sin (k z-\omega t) \hat{j}$
a) evaluate $\oint E . d l \quad$ over the rectangular loop 1234 shown in the figure
b) evaluate $\int B \cdot d s$ over the surface bounded by loop 1234
CBSE | Class 12 | Electromagnetic Waves | ncert exemplar | Physics
A plane EM wave travelling in vacuum along z-direction is given by $E=E_{0} \sin (k z-\omega t) \hat{i} \text { and } B=B_{0} \sin (k z-\omega t) \hat{j}$
a) evaluate $\oint E . d l \quad$ over the rectangular loop 1234 shown in the figure
b) evaluate $\int B \cdot d s$ over the surface bounded by loop 1234

Solution:

(a) $\oint_{\vec{E}} \cdot \overrightarrow{d l}=E_{0} h\left[\sin \left(k z_{2}-\omega t\right)-\sin \left(k z_{1}-\omega t\right)\right]$

(b) $\int \vec{B}.{\overrightarrow{d s}} = \frac{\vec{d}_{0} h}{k}\left[\cos \left(k z_{2}-\omega t\right)-\cos \left(k z_{1}-\omega t\right)\right]$

 

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