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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 60βΈ° 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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