A coil of 10.0 turns is in the shape of an ellipse having a major axis of 10.0 c

Question

A coil of 10.0 turns is in the shape of an ellipse having a
major axis of 10.0 cm and a minor axis of 4.00 cm. The coil rotates at 100 rpm
in a region in which the magnitude coil rotates at 100 rpm in a region in which
the magnitude of Earth’s magnetic field is 55 T. 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 (a) perpendicular to Earth’s magnetic field and (b)
parallel to Earth’s magnetic field? (Note: the area of an ellipse is given by
A=(pi)(a)(b), where a is the length of the semimajor axis and b is the length
of the semiminor axis.)

Provide full Explanation and solution. The answers at the
back of the book are: (a) 18.1 V (b) 0

Explanation / Answer

Part A)

The formula for the max induced EMF is

= NBA

A = ab   where a and b are half of the major and minor axes (.05 m and .02 m)

= 100 rpm and it must be converted to rad/s (2 rad per rev and 60 sec per min)

= (10)(55 X 10-6)()(.05)(.02)(100)(2)/60

= 1.81 X 10-5 V   which is 18.1 V

Part B)

The answer is zero since the area and the magnetic field are parallel. You can only have induced voltages if a component between the area an the magnetic field is greater than 0 degrees.

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