Square Loop and Magnetic Forces

[ecthelion4]

I need to prove that the magnetic force done to a square loop with a current by an uniform magnetic field is zero. The exact problem is this:

A square loop of sides of length l and carrying a current I lies at the xy plane in the presence of a uniform magnetic field B(vector) = B<. Show by calculating explicitly the magnetic force vector on each segment and then adding all the vectors that the magnetic force is 0

I'm pretty sure you can calculate the force on a wire segment with F=(current through wire)(length of wire)x(magnetic field). Can I apply that in this problem or would a different approach be more suitable? The problem also states that I need to calculate a torque, I honestly have no idea WHERE I can do that in this problem.

 

[Doc Al]

I'm pretty sure you can calculate the force on a wire segment with F=(current through wire)(length of wire)x(magnetic field). Can I apply that in this problem or would a different approach be more suitable?

Yes, use that to calculate the force on each segment.

The problem also states that I need to calculate a torque, I honestly have no idea WHERE I can do that in this problem.

Depending on the direction of the field, there may be a net torque on the loop.

 

[ogb p]

I would approach this problem by first understanding the basic principles of magnetic forces and how they act on a current-carrying loop. The magnetic force on a segment of wire can be calculated using the formula F = I * L * B, where I is the current, L is the length of the wire segment, and B is the magnetic field. This formula can be used for each segment of the square loop to calculate the individual magnetic forces.

Next, I would consider the direction of the magnetic force on each segment. Since the magnetic field is uniform, the force on each segment will be in the same direction. However, due to the symmetry of the square loop, the forces on opposite sides will be equal and opposite, resulting in a net force of zero.

To further prove this, I would calculate the torque on the square loop. Torque is defined as the cross product of the force and the distance from the axis of rotation. In this case, the axis of rotation would be the center of the square loop. Since the magnetic force on each segment is parallel to the distance from the axis, the torque will also be zero.

In conclusion, using the principles of magnetic forces and the symmetry of the square loop, it can be proven that the magnetic force on the loop is zero. This is also supported by the fact that the torque on the loop is also zero. Therefore, the magnetic force done on the square loop by a uniform magnetic field is indeed zero.