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A circular coil consisting of 500 turns with an area of 6.0x10-4 m 2 is rotating in a uniform magnetic field. At the start, the normal to the coil is perpendicular to the magnetic field. After 15s, the normal to the coil is 60⸰ with the magnetic field. The average induced emf is -0.058V. What is the magnitude of the magnetic field?

Respuesta :

onyebuchinnaji

The magnitude of the magnetic field in the coil is 21.65 T.

The given parameters;

  • number of turns, N = 500 turns
  • area of the coil, A = [tex]6\times 10^{-4} \ m^2[/tex]
  • change in time, t = 15 s

The induced emf in the coil is determined by applying Faradays law;

[tex]emf =N \frac{d\phi }{dt} \\\\emf = N ( \frac{\phi _2 - \phi_1}{t} )\\\\emf= N(\frac{BAsin\ 60 - BAsin\ 90}{t} )\\\\emf = NBA(\frac{sin60 - sn90}{t} )\\\\-0.058 = 500(6\times 10^{-4})\times B\times (\frac{0.866 - 1}{15} )\\\\-0.058 = -0.00268B\\\\B = \frac{0.058}{0.00268} \\\\B = 21.65 \ T[/tex]

Thus, the magnitude of the magnetic field in the coil is 21.65 T.

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