1. One practical way to measure magnetic field strength uses a small, closely wo

Question

1. One practical way to measure magnetic field strength uses a small, closely would coil called a search coil. The coil is initially held with its plane perpendicular to a magnetic field. The coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. Derive the equation relating the total charge Q that flows through a search coil to the magnetic-field magnitude B. The search coil has N turns, each with area A, and the flux through the coil is decreased from its initial maximum value to zero in a time ?t. The resistance of the coil is R, and the total charge is Q = I?t, where I is the average current induced by the change in flux. (Note: A credit-card reader works by having you

Explanation / Answer

The Induced EMF formula is

= IR = N/t

Since I = Q/t and = BA, we can substitute

(Q/t)(R) = NBA/t     (t cancels)

QR = NBA

So...

Q = NBA/R

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