A piece of insulated wire is shaped into a figure eight as shown in the figure...

A piece of insulated wire is shaped into a figure eight as shown in the figure below. For simplicity, model the two halves of the figure eight as circles. The radius of the upper circle is 4.00 cm and that of the lower circle is 8.00 cm. The wire has a uniform resistance per unit length of 7.00 Ω/m. A uniform magnetic field is applied perpendicular to the plane of the two circles, in the direction shown. The magnetic field is increasing at a constant rate of 1.60 T/s.

Solutions

Expert Solution

Resistance per unit length is

Rate of increase in magnetic field

Radius of upper circle

Radius of lower circle

Resistance of the wire is

Flux through the wire is

For lower circle

For upper circle

Induced EMF Induced current is

The magnetic field is increasing and is into the page, By Lenz's law the direction of current opposes the changing magnetic field that produced it. So for the larger circle direction of induced current is counter clockwise and so for the smaller upper loop its direction is clockwise.

Direction of induced current is counter clockwise in lower loop , and clockwise in upper loop.

genius_generous answered 1 year ago

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