What is the torque on the current loop?

+1 vote

A rectangular loop of wire has dimensions 0.475 m by 0.273 m. The loop is pivoted at the x axis and lies in the xy plane as shown in the figure below. A uniform magnetic field of magnitude 1.46 T is directed at an angle of 40.0° with respect to the y axis with field lines parallel to the yz plane. The loop carries a current of 0.918 A in the direction shown. (Ignore gravitation.) We wish to evaluate the torque on the current loop.

image
(a) What is the direction of the magnetic force exerted on wire segment ab?


(b) What is the direction of the torque associated with this force about an axis through the origin?


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


(d) What is the direction of the torque associated with this force about an axis through the origin?


(e) Can the forces examined in parts (a) and (c) combine to cause the loop to rotate around the x axis?


(f) Can they affect the motion of the loop in any way?


Explain.

(g) What is the direction of the magnetic force exerted on segment bc?


(h) What is the direction of the torque associated with this force about an axis through the origin?


(i) What is the torque on segment ad about an axis through the origin?


(j) From the point of view of the figure above, once the loop is released from rest at the position shown, will it rotate clockwise or counterclockwise around the x axis?


(k) Compute the magnitude of the magnetic moment of the loop.
A · m2

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

(m) Compute the torque on the loop using the results to parts (k) and (l).
N · m 
asked Feb 19, 2012 in Physics by apush ~Expert~ (552 points)
    

1 Answer

0 votes
The direction of the magnetic force can be found by applying the right hand rule.

When using the right hand rule, your fingers point in the direction of the field, and the thumb points in the direction of the current.  Whichever direction your palm is facing is the direction of the force (force is the cross product of the two vectors).

You can see that in this problem the current is traveling clockwise in the wire.

So for Part A,

the current is going from a to b, and so have your thumb point from a to b. Next point your fingers in the direction of the field, which is pointing upwards.  Therefore your palm should be pointing in the positive x direction.

Similarily, the direction of torque can also be determined using the right hand rule. Since the torque is the cross product of Magnetic Moment (*which is current*area) and magnetic field.

So once again start by having the thumb point from the axis towards the current flow direction, in Part B this would be from origin to point b direction.

Next, point your fingers in the direction of force (*not field, since this is torque), force is in x direction.

And so your palm should be facing in the negative z direction, the direction of the torque.

Parts C and D can be solve similarily.

 

Part E,

the answer is no, because the forces basicically cancel each other out.

Part F,

Also No, same reason as part E.
answered Feb 24, 2012 by pokemonmaster ~Expert~ (3,856 points)
edited Feb 24, 2012 by pokemonmaster



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