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

A coil of 12 turns is in the shape of an ellipse having a major axis of 20.2 cm and a minor axis of 9.82 cm. The coil rotates at 94 rpm in a region in which the Earth's magnetic field is 56.2 μT. 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?

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Answer #1

Area of the ellipse will be

Where is semi-major axis and is the semi-minor axis.

When  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, then flux will be

Where is angle between area vector and B. Now angular velocity is given as  

Then induced EMF will be

For maximum EMF, hence

(b) When 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, there will not be the change in the flux as area vector will always be perpendicular to the field hence induced EMF will be zero.

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