Question

Calculating the force on a current loop in a magnetic field is more subtle than on a single straight wire. 1) The net force on a current loop in a uniform magnetic field is zero. Argue why this is so using the rectangular loop in the field shown to the right. Assume that the current flows clockwise around the loop. Show forces on the diagram. (Hint: Consider the magnitude and direction of the force on each side of the loop.) The net force on a loop is not necessarily zero if the magnetic field is not uniform. In this section you will calculate the net force on current in a circular loop in a diverging magnetic field. Recall for a bar magnet, that the magnetic fields at each end of the magnet are diverging as illustrated in the sketch. Consider a circular loop of radius R, carrying current I in a magnetic field pointing to the right. At the loop, the top magnetic field vector B is 10 degrees above horizontal and the bottom magnetic field vector B is 10 degrees below horizontal. The observer on the right sees the current going in the clockwise direction. 2) Sketch a force vector at the top and bottom of the circular loop. 3) What is the magnitude of the horizontal component of the force on a small length of wire ds at the top of the loop? (Note that the vertical components of force should have canceled with each other in your sketch.) 4) Integrate over the length of the loop to find the net force on the loop. 5) Does the force increase or decrease as the coil is moved to the right? Explain your response.

Calculating the force on a current loop in a magnetic field is
more subtle than on a single straight wire.
1) The net force on a current loop in a uniform magnetic field
is zero. Argue why this is so using the rectangular loop in
the field shown to the right. Assume that the current flows
clockwise around the loop. Show forces on the diagram.
(Hint: Consider the magnitude and direction of the force on
each side of the loop.)
The net force on a loop is not necessarily zero if the magnetic
field is not uniform. In this section you will calculate the net force on current in a
circular loop in a diverging magnetic field. Recall for a bar magnet, that the
magnetic fields at each end of the magnet are diverging as illustrated in the
sketch.
Consider a circular loop of radius R, carrying current I in a magnetic field
pointing to the right. At the loop, the top magnetic field vector B is
10 degrees above horizontal and the bottom magnetic field vector B is
10 degrees below horizontal. The observer on the right sees the current
going in the clockwise direction.
2) Sketch a force vector at the top and bottom of the circular loop.
3) What is the magnitude of the horizontal component of the force on a
small length of wire ds at the top of the loop? (Note that the vertical
components of force should have canceled with each other in your
sketch.)
4) Integrate over the length of the loop to find the net force on the loop.
5) Does the force increase or decrease as the coil is moved to the right? Explain your response.

Added by Lance C.

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