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A plane electromagnetic wave of frequency 24 MHz travels in free space along the x-direction. At a particular point in space and time ⃗E = 6.3 ̂j V m⁻¹. The value of ⃗B at this point will be _______.

Asked in GSEB Board August 2020 · Writing B from E, and E from B

• (1) -2.1×10⁻⁸ ̂k T
• (2) -2.1×10⁻⁸ ̂j T
• (3) 2.1×10⁻⁸ ̂k T
• (4) 2.1×10⁻⁸ ̂j T

Step-by-step solution

Why the other options are wrong

• (1) The magnitude is right but the sense is reversed. With ⃗E along +̂j and ⃗B along -̂k, ̂E×̂B points along -̂i, so this would be a wave travelling in the -x direction.
• (2) Here ⃗B is put on the same axis as ⃗E and opposed to it. In a plane electromagnetic wave ⃗E and ⃗B are always perpendicular, and they are in phase, so they are never antiparallel.
• (4) Here ⃗B is put parallel to ⃗E. Then ̂E×̂B = 0, and the wave would have no direction of propagation at all.

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