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A plane electromagnetic wave of wavelength λ has an intensity I. It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by - [JEE-Main On line-2018]

1. E=√((I)/(ε₀ c))cos [(2π)/(λ)(y-ct) ]î; B=(1)/(c)Ek̂
2. E=√((I)/(ε₀ c))cos [(2π)/(λ)(y-ct) ]k̂; B=(1)/(c)Eî
3. E=√((2I)/(ε₀ c))cos [(2π)/(λ)(y-ct) ]k̂; B=±(1)/(c)Eî
4. E=√((2I)/(ε₀ c))cos [(2π)/(λ)(y+ct) ]î; B=(1)/(c)Eî

Correct answer: E=√((2I)/(ε₀ c))cos [(2π)/(λ)(y-ct) ]k̂; B=±(1)/(c)Eî

Solution

Intensity I = (1/2) eps0 c E0^2 gives E0 = sqrt(2I/(eps0 c)). For propagation along +y with E along z (k-hat) and B along x (i-hat), E x B points +y. Thus E = sqrt(2I/(eps0 c)) cos[(2pi/lambda)(y-ct)] k-hat, B = +-(1/c)E i-hat.

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