A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time ⃗B = 2.1×10⁻⁸ ̂k T. Find ⃗E at this point.

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(2) 6.3 ̂j V m⁻¹. Given: B = 2.1×10⁻⁸ T along ̂k, wave travelling along +x in free space. Idea: in a plane electromagnetic wave the magnitudes obey E = cB, and ⃗E, ⃗B and the direction of travel form a right-handed set, with ̂E×̂B pointing along the direction of travel. Magnitude: E = cB = (3×10⁸)(2.1×10⁻⁸) = 6.3 V m⁻¹. Direction: we need ̂E×̂k = ̂i, and ̂j×̂k = ̂i, so ⃗E lies along ̂j. So ⃗E = 6.3 ̂j V m⁻¹; the frequency is not needed.

A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time ⃗B = 2.1×10⁻⁸ ̂k T. Find ⃗E at this point.

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