The time varying electric and magentic fields are E-Ex-Ex-Ezk- and B-Bx-By-Bzk- respectively- They generate a plane electromagnetic wave travelling towards x-direction in pair of space-

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Wave Equation of EM Waves

The time vary...

Question

The time varying electric and magentic fields are $E = E_{x}^i + E_{x}^j + E_{z}^k$ and $B = B_{x}^i + B_{y}^j + B_{z}^k$ respectively. They generate a plane electromagnetic wave travelling towards x-direction in pair of space.

E_{y}, B_{z}

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E_{x}, B_{y}

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E_{z}, B_{x}

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E_{z}, B_{z}

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Solution

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\to B = B_{x}^i + B_{y}^j + B_{z}^k

\to E = E_{x}^i + E_{y}^j + E_{z}^k

\to u = u_{x}^i + u_{y}^j + u_{z}^k

E = 0

u_{x} B_{x} + u_{y} B_{y} \neq - u_{z} B_{z}

\to B = B_{x}^i + B_{y}^j + B_{z}^k

\to E = E_{r}^i + E_{y}^j + E_{z}^k

\to u = u_{x}^i + u_{y}^j + u_{z}^k

\to u \times \to B = 0

\to u \times \to E = 0

E = (i E_{x} + j E_{y} + k E_{z})

B = (i B_{x} + j B_{y} + k B_{z})

E x = 0, E y = 0,

E_{Z} = 2.5 ((2 π \times 10^{6}) t - (π \times 10^{- 2}) x]

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