   Chapter 19, Problem 41P

Chapter
Section
Textbook Problem

Along piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40-A current, and is placed in a vertical magnetic field with a magnitude of 0.010 0 T. (a) Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. (b) Find the torque acting on the coil due to the magnetic force at equilibrium.

a)

To determine
The angle that the plane of the coil makes with the vertical when the coil is in equilibrium.

Explanation

Given info: The mass of the wire is 0.100kg . The total length of the wire is 4.00m . The side of the square coil is 0.100m . The coil carries a current of 3.40A and hinged along the horizontal side. The magnetic field is vertical and has a magnitude of 0.0100T .

Explanation:

The given system is shown in the following Figure 1.

The torque about the z-axis due to gravity is,

τg=mg(s2)cosθ

• m is mass of the coil
• g is the free fall acceleration
• θ is the angle between plane of the loop and the horizontal
• s is the length of one side of the loop

The torque due to the magnetic force is given by,

τm=NIBAsinθ

• I is the current in the wire
• N is the number of loops in the coil
• B is the magnetic field
• A is the area enclosed by the loop
• θ is the angle between the magnetic field and the direction of current flow

The torque due to gravitational force tend to rotate the coil clockwise, where as the torque due to the magnetic force tend to rotate the coil anticlockwise.

At equilibrium both the torque will be equal,

mg(s2)cosθ=NIBAsinθ

On re-arrangement,

tanθ=mgs2NIBA

But the area of the coil will be s2 . Hence,

tanθ=mgs2NIBs2=mg2NIBs       (1)

The number of coil will be the ratio of the length of the wire and the circumference of the coil

b)

To determine
The torque acting on the coil due to the magnetic force at equilibrium.

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