A coil of 12 turns is in the shape of an ellipse having a major axis of 11.0 cm

Question

A coil of 12 turns is in the shape of an ellipse having a major axis of 11.0 cm and a minor axis of 5.00 cm. The coil rotates at 134rpm in a region in which the Earth's magnetic field is 58.0 microT. What is the maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and this axis of rotation is aligned perpendicular to the Earth's magnetic field?

What is the maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and this axis of rotation is aligned parallel to the Earth's magnetic field?

Explanation / Answer

The total area of the coil as far as the magnetic flux calculation is concerned is |A| = 12 turns *pi *a*b = 12*172.79 cm² = 2073.48 cm^2 = 0.207348 m^2.

magnetic flux

w = 2* pi *134/60 = 14.032 rad/s
= B dot A = |B| |A| cos( w t )

The time derivative of this expression is:

'(t) = - |B| |A|w sin( w t ).

At the maximum of sine, it equals 1. According to Faraday's law, this means a maximum induced EMF of:

V = w |A| |B|

=14.03*0.207348*58*10^-6

maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and this axis of rotation is aligned perpendicular to the Earth's magnetic field=1.6875*10^-4 v

2. if the axis of rotation is parallel to magnetic field then enduced emf is 0 as sin o become 0

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