A 0.230 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of 10,000 V.

Question

Physics

Charlie Santana

17 July, 09:58

A 0.230 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of 10,000 V.

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Answers (1)

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Addison Hill · Answer 1

0.5 T

Explanation:

Parameters given:

Time, t = 4.17 ms = 0.00417 s

Number of turns, N = 500 turns

Radius, r = 0.23 m

EMF = 10000 V

The formula for EMF induced by a magnetic field, B, in a coil or area A is given as:

EMF = (B * N * A) / t

Area, A is given as:

A = pi * r² = 3.142 * 0.23²

A = 0.166 m²

=> 10000 = (B * 500 * 0.166) / 0.00417

=> B = (10000 * 0.00417) / (500 * 0.166)

B = 0.5 T