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Loop of wire spun at an angular rate about a vertical axis: EMF and current induced

A 5 meter long copper wire, with a cross sectional area of 1.0mm^2 is bent into a circle. This loop of wire is mounted in a vertical plane between the poles of a magnet. This magnet is aligned so that its field points in a horizontal direction from the west to the east; the magnitude of this field is 7.25*10^(-4)T. The loop of wire is then spun at an angular rate of 10pi radians/sec about a vertical axis running through the center of the loop.

1) What emf is induced?

2) What current is induced in the wire?

Solution Preview

Because, induced EMF (e)= -d(phi)/d(t)
here negative sign shows that induced emf opposes the cause of it's inductin.
phi = magnetic flux = B*A
A = area of circle.
The area of circle crossing the magnetic field line will change with time because, it is rotated with respect to vertical axis.
hence,
d(phi)/dt = B*dA/dt
because, let ...

Solution Summary

With good explanations and calculations, the problems are solved.

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