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The magnetic field in a plane electromagnetic wave is given by  \(B=(2\times 10^{\text{--}7}T\sin (0.5\times 10^3x+1.5\times 10^{11}t)\) .Write an expression for the electric field.

Answer

\(E_z=60\sin (0.5\times 10^3x+1.5\times 10^{11}t)V/m\)
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Solution

Given:
\(B=(2\times 10^{\text{--}7}T\sin (0.5\times 10^3x+1.5\times 10^{11}t)\)
\(B_0=2\times 10^{-7}\;T\)
\(c=3\times 10^8\;m/s\)
\(E_0=B_Oc=2\times 10^{-7}\times 3\times 10^8=6\times 10^1V/m\)
The electric field component is perpendicular to the direction of propoagation and the direction of magnetic field. Therefore, the electric field component along the \(z-\)axis is obtained as
 \(E_z=60\sin (0.5\times 10^3x+1.5\times 10^{11}t)V/m\) 
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