Torque by magnetic field on a current carrying wire loop ?

In summary, torque is given by NI(A X B) where N and I are number of loop turns and current magnitude respectively, A is area in vector and B is magnetic field in vector. The direction of the area vector can be determined by either approach A, where the current is always treated as positive and the direction of the area vector is taken as the direction of circulation of the current, or approach B, where the direction of the area vector is defined by an arbitrary agreed sense around the loop. The current, I, can be positive or negative depending on the direction of circulation. It is also important to keep in mind the general points for handling cross products of vectors.
  • #1
mohamed el teir
88
1
as u know torque is given by NI(A X B) where N and I are number of loop turns and current magnitude respectively, A is area in vector and B is magnetic field in vector. regarding the direction of area : what normal to take as a direction, is at that which makes acute angle with magnetic field (supposing that magnetic field has a specific direction) ? and if the normal to the area is perpendicular to the field so which normal to choose then ? and does the equation of the torque indicate that its direction is independent from the direction of current ?
 
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  • #2
This is a very good question. The handling of this sort of thing causes a lot of confusion, largely because there are at least two approaches.

Approach A (used in more elementary work)

The current, I, is treated as always positive, and the direction of the area vector is taken as the direction in which a right handed screw would advance if turned in the direction of circulation of the current.

Approach B
(preferred especially in more advanced work)

The direction of the area vector is defined to be that in which a right handed screw would advance if turned in the same sense as that of an arbitrary agreed sense around the loop (e.g. ABCDA, if A, B, C and D are points in cyclic order around the loop). This is a purely geometric convention, independent of currents etc.

The current, I, although not a vector, can be positive or negative and we take it as positive if it's circulating in the sense ABCDA and negative if in the sense ADCBA.

This is all you need for the vector relationship you quote to deliver the goods, with the direction of the current taken care of by the sign of I. You'll find it gives you the same direction of torque whichever way round you put A, B, C and D in setting up the geometrical convention.

General points for handling cross products of vectors. (1) Imagine rotating the first vector like a spanner (wrench) through the smaller angle to make it lie in the same direction as the second. Direction of product vector is the direction in which a right handed bolt would advance when gripped by the spanner. (2) a minus sign in front of a vector (that is multiplication of the vector by the scalar –1) gives a vector of the same magnitude in the reverse direction.

Hope this helps.
 
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Related to Torque by magnetic field on a current carrying wire loop ?

1. What is torque by magnetic field on a current carrying wire loop?

Torque by magnetic field on a current carrying wire loop refers to the rotational force experienced by a wire loop when it is placed in a magnetic field and has an electric current passing through it. This torque is caused by the interaction between the magnetic field and the electric current, and it causes the loop to rotate.

2. How is the direction of torque determined?

The direction of torque by magnetic field on a current carrying wire loop is determined by the right-hand rule. This rule states that if you point your thumb in the direction of the current, and your fingers in the direction of the magnetic field, the direction of the torque will be perpendicular to both your thumb and fingers.

3. What factors affect the magnitude of torque by magnetic field on a current carrying wire loop?

The magnitude of torque by magnetic field on a current carrying wire loop depends on several factors, including the strength of the magnetic field, the amount of current flowing through the wire, the length of the wire, and the angle between the wire and the magnetic field.

4. How is torque by magnetic field on a current carrying wire loop used in practical applications?

This phenomenon is used in a variety of practical applications, such as electric motors, generators, and magnetic levitation systems. In electric motors, the torque generated by the interaction between the magnetic field and the current causes the motor to rotate, which can then be used to power machinery. In generators, the opposite occurs, as the rotation of the wire loop in the magnetic field creates an electric current.

5. Can torque by magnetic field on a current carrying wire loop be negative?

Yes, torque by magnetic field on a current carrying wire loop can be negative. This occurs when the direction of the magnetic field or the current is reversed, causing the direction of the torque to also reverse. In this case, the wire loop will rotate in the opposite direction as before.

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