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  • The electric field of a plane polarized electromagnetic wave in free space at time  t = 0 is given by an expression

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The electric field of a plane polarized electromagnetic wave in free space at time  t = 0 is given by an expression \vec{E}\left ( x,y \right )= 10 \hat{j}\cos \left [ \left ( 6x +8z\right ) \right ]

The magnetic field field \vec{B} \left ( x,z,t \right ) is given by :( c is the velocity of light)

Answers (1)

best_answer

For a A plane EM wave traveling in the x-direction is of the form

\vec{E}\left ( x,y \right )= 10 \hat{j}\cos \left [ \left ( 6x +8z\right ) \right ]

 \vec{B} \left ( x,z,t \right )=B_0\cos \left [ \left ( 6x +8z\right ) \right ] .........(1)

and B_0=\frac{E_0}{c}

So option 2 and 3 does not equation 1

Now E is in the direction of \vec{j}

similalay direction of wave is along \alpha \vec{i}+\beta \vec{k}

and The direction of propagation is the direction of E x B.

So for option 1

B=\frac{1}{c}\left ( 6\hat{k}-8\hat{i} \right )\cos \left [ \left ( 6x+8z-10ct \right ) \right ]

B is in direction B=\frac{1}{c}\left ( 6\hat{k}-8\hat{i} \right )

and for this option E x B is along \alpha \vec{i}+\beta \vec{k}

So correct option is 1.

Posted by

avinash.dongre

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