Question

A rectangular loop has dimensions 0.505 m by 0.260 m. The loop is hinged along the x-axis and lies in the xy-plane (see the figure below). A uniform magnetic field of 1.45 T is directed at an angle of 40.0° with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The loop carries a current of 0.855 A in the direction shown. (Ignore gravitation.)

(a) In what direction is magnetic force exerted on wire segment ab?
direction

What is the direction of the magnetic torque associated with this force, as computed with respect to the x-axis?
direction

(b) What is the direction of the magnetic force exerted on segment cd?
direction

What is the direction of the magnetic torque associated with this force, again computed with respect to the x-axis?
direction

(c) Can the forces examined in parts (a) and (b) combine to cause the loop to rotate around the x-axis? Can they affect the motion of the loop in any way? Explain.
This answer has not been graded yet.

(d) What is the direction (in the yz-plane) of the magnetic force exerted on segment bc?

° counterclockwise from the +y-axis

Measuring torques with respect to the x-axis, what is the direction of the torque exerted by the force on segment bc?
direction

(e) Looking toward the origin along the positive x-axis, will the loop rotate clockwise or counterclockwise?

(f) Compute the magnitude of the magnetic moment of the loop.

A · m2

(g) What is the angle between the magnetic moment vector and the magnetic field?

° counterclockwise from the magnetic moment vector

(h) Compute the torque on the loop using the values found for the magnetic moment and magnetic field.

N · m

Answer 1

a )

here the current in ab segment og y-direction.

using right hand rule, the B value in x - direction, so then the force is parallel to x - axis. so the

torque is in that axis.

b )

here the current in cd segment in y - direction.

same way the right hand rule says that B value in -ve x - direction, force is parallel to x axis.

so no torque will be calculated.

c )

here in this case,

each force have zero torque, so that they can have no effect on the motion of loop.

d )

B value is in perpendicular to both the direction of current in bc of x-direction.

in yz plane at 130^o anti clockwise from y - axis.

so the torque is in x -direction.

e )

here loop rotates in anti clockwise of x axis.

f )

$\mu$ = i A N

= 0.505 x 0.260 x 0.855

$\mu$ = 0.1122 A.m²

g )

the angle is = 90 + 40

= 130^o

h )

_T = $\mu$ B sin130

= 0.1122 x 1.45 x sin130

_T = 0.1246 N.m