Practice portal › Electromagnetic Waves › The Plane Wave: Reading the Equation

The electric field component of a monochromatic radiation is given by E⃗ = 2E₀ ı̂ cos kz cos ω t. Its magnetic field is then given by

Asked in JEE Main Online 2017 · Direction of travel and standing waves

• (1) (2E₀)/c ȷ̂ cos kz cos ω t
• (2) (2E₀)/c ȷ̂ sin kz cos ω t
• (3) (2E₀)/c ȷ̂ sin kz sin ω t
• (4) -(2E₀)/c ȷ̂ sin kz sin ω t

Step-by-step solution

Why the other options are wrong

• (1) comes from this just copies E's own factors cos kz cos ω t; both must change
• (2) comes from the space factor sin kz is right, but the time factor becomes sin ω t after integrating cos ω t
• (4) comes from correct form but with an overall minus sign; abla × E⃗ = -∂B⃗/∂ t gives +(2E₀/c)

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