   Chapter 19, Problem 38P

Chapter
Section
Textbook Problem

A current-carrying rectangular wire loop with width a = 0.120 m and length b = 0.200 m is in the xy-plane, supported by a non-conducting, frictionless axle of negligible weight A current of I = 3.00 A travels counterclockwise in the circuit (Fig. P19.38). Calculate the magnitude and direction of the force exerted on the (a) left and (b) right segments of wire by a uniform magnetic field of 0.250 T that points in the positive x- direction. Find the magnetic force exerted on the (c) top and (d) bottom segments. (e) Find the magnitude of the net torque on the loop about the axle. Figure P19.38

(a)

To determine

The magnitude and direction of force exerted on the left segment of the wire.

Explanation

Given Info: The width of the rectangular loop is a=0.120m. The length of the loop is b=0.200m. The loop is in xy-plane. The current of magnitude 3.00A travels counterclockwise in the circuit. The magnitude of the magnetic field is 0.250T and it points in the positive x-direction.

The magnetic force on a current carrying conductor is given by,

Fm=BILsinθ

• B is the magnetic field
• L is the length of the conductor
• I is the current flowing in the conductor
• θ is the angle between the magnetic field and the current direction

Since the magnetic field is perpendicular to the loop, the magnetic force on the left segment will be,

Fm=BIb

Substitute 0.250T for B, 3

(b)

To determine

The magnitude and direction of force exerted on the right segment of the wire.

c)

To determine

The magnitude and direction of force exerted on the top segment of the wire.

d)

To determine

The magnitude and direction of force exerted on the bottom segment of the wire.

e)

To determine

The torque on the loop.

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