Figure P19.64 is a setup that can be used to measure

Chapter 19, Problem 19.97

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Figure P19.64 is a setup that can be used to measure magnetic fi elds. A rectangular coil of wire contains N turns has a width w. The coil is attached to one arm of a balance and is suspended between the poles of a magnet. The fi eld is uniform and perpendicular to the plane of the coil. The system is fi rst 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 fi eld 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 fi eld?