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  • A plane electromagnetic wave propagating in the -direction has wavelength of <img alt="6.0 \mathrm{~mm

A plane electromagnetic wave propagating in the \mathrm{x}-direction has wavelength of 6.0 \mathrm{~mm}. The electric field is in the \mathrm{y}-direction and its maximum magnitude of 33 \mathrm{Vm}^{-1}. The equation for the electric field as function of \mathrm{\mathrm{x} \: and\: t} is:
 

Option: 1

11 \sin \pi(\mathrm{t}-\mathrm{x} / \mathrm{c})



 


Option: 2

33 \sin \pi \times 10^{11}(\mathrm{t}-\mathrm{x} / \mathrm{c})


Option: 3

\mathrm{33 \sin \pi(t-x / c)}


Option: 4

11 \sin \pi \times 10^{11}(\mathrm{t}-\mathrm{x} / \mathrm{c})


Answers (1)

Angular frequency, \omega=2 \pi \mathrm{v}=\frac{2 \pi \mathrm{c}}{\lambda} \quad \quad [\because \quad \mathrm{v}=\mathrm{c} / \lambda]

\mathrm{ =\frac{2 \pi \times 3 \times 10^8}{6 \times 10^{-3}}=\pi \times 10^{11} \mathrm{rads}^{-1} }

The equation for the electric field, along \mathrm{Y}-axis in the electromagnetic wave is

\mathrm{ \mathrm{E}_{\mathrm{y}}=\mathrm{E}_0 \sin \omega\left(\mathrm{t}-\frac{\mathrm{x}}{\mathrm{c}}\right)=33 \sin \pi \times 10^{11}(\mathrm{t}-\mathrm{x} / \mathrm{c}) }

Hence option 2 is correct.


 

Posted by

Kshitij

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