The figure below shows a schematic representation of an apparatus that can be us

Question

The figure below shows a schematic representation of an apparatus 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 magnetic 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. (Use any variable or symbol stated above along with the following as necessary: g.)
B =

(b) Why is the result independent of the vertical dimensions of the coil

(c) Suppose the coil has 56 turns and a width of 4.80 cm. When the switch is closed, the coil carries a current of 0.330 A, and a mass of 18.6 g must be added to the right side to balance the system. What is the magnitude of the magnetic field?
(in T)

The figure below shows a schematic representation of an apparatus 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 magnetic 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. (Use any variable or symbol stated above along with the following as necessary: g.) B = (b) Why is the result independent of the vertical dimensions of the coil (c) Suppose the coil has 56 turns and a width of 4.80 cm. When the switch is closed, the coil carries a current of 0.330 A, and a mass of 18.6 g must be added to the right side to balance the system. What is the magnitude of the magnetic field? (in T)

Explanation / Answer

magnetic force F = iLB

and gravtitaional force F = mg

so

equating both forces

mg = N iLB

so

magnetic field B = mg/iL N

where i is current

g is accleration due to gravity

m is mass

and L is length

so

EQUATION FOR MAGNETIC FIELD B = mg/iL N

-----------------------

part C:

B = 18.6 e-3 * 9.8/(0.330 * 56 * 0.048)

B = 0.2054 Tesla

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