Figure P19.64 is a setup that can be used to measure
magnetic fields. A rectangular coil of wire contains N turns
and has a width w. The coil is attached to one arm of a balance
and is suspended between the poles of a magnet. The field
is uniform and perpendicular to the plane of the coil. The
system is first balanced when the current in the coil is zero.
When the switch is closed and the coil carries a current I, a
mass m must be added to the right side to balance the system.
(a) Find an expression for the magnitude of the magnetic
field and determine its direction. (b) Why is the result independent
of the vertical dimension of the coil? (c) Suppose
the coil has 50 turns and width of 5.0 cm. When the switch is
closed, the coil carries a current of 0.30 A, and a mass of 20.0 g
must be added to the right side to balance the system. What is
the magnitude of the magnetic field?
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