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

Question

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 /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.

(a) Find the magnitude of the induced current in the wire.

_____A

webassign is marking my answer as 0.001 wrong. not sure what else it could be.

Explanation / Answer

Pick a direction for the current to be counterclockwise in the bottom loop (so clockwise in the top). Thus, the area vector of the top
loop is antiparallel to B and that of the bottom loop is parallel to B. The magnetic flux is then

B = A·B = (r2s r2b)B

So using Ampere’s law

= dB/dt= (r2b r2s)dB/dt

The resistance of the entire figure eight is

R = (2rs +2rb)

And plugging that into Ohm’s law

= V = IR

I =(r2b r2s)dB/dt/2(rs +rb)
= 0.0000457

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