A coil of 6.0 turns is in the shape of an ellipse having a major axis of 12.0 cm

Question

A coil of 6.0 turns is in the shape of an ellipse having a major axis of 12.0 cm and a minor axis of 5.00 cm. The coil rotates at 103 rpm in a region in which the magnitude of the Earth's magnetic field is 55 µT. What is the maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and is aligned in the following directions.
(a) perpendicular to the Earth's magnetic field
µV
(b) parallel to the Earth's magnetic field
V
(Note that the area of an ellipse is given by A = pab, where a is the length of the semimajor axis and b is the length of the semiminor axis.)

Explanation / Answer

Given that Magnetic field B = 55*10^-6 T Number of turns N = 6 Area A = 0.12 * 0.05 = 0.006 m^2 By Faraday's Law Induced voltage E = - /t        The total flux through the coil = N B A     = 9 * 55 *10^-6 *0.006     = 2.97 * 10^-6 weber (tesla-m2) P (period) = 1 / f = 1 /103 = 0.0097 min = 0.582 sec Flux goes from min to max in 1/4 revolution t = P / 4  = 0.1456 sec    E = 2.97 * 10^-6 /  0.1456 =20.394 * 10^-6 V = 20.394 V b)If the axis of the coil is parallel to the magnetic field then no flux passes through the coil and hence there is no induced Emf. ZERO Given that Magnetic field B = 55*10^-6 T Number of turns N = 6 Area A = 0.12 * 0.05 = 0.006 m^2 By Faraday's Law Induced voltage E = - /t        The total flux through the coil = N B A     = 9 * 55 *10^-6 *0.006     = 2.97 * 10^-6 weber (tesla-m2) P (period) = 1 / f = 1 /103 = 0.0097 min = 0.582 sec Flux goes from min to max in 1/4 revolution t = P / 4  = 0.1456 sec    E = 2.97 * 10^-6 /  0.1456 =20.394 * 10^-6 V = 20.394 V b)If the axis of the coil is parallel to the magnetic field then no flux passes through the coil and hence there is no induced Emf. ZERO

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