Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A small square loop carries a current and hangs in a uniform magnetic field. (a) The forces on its four sides add to zero. Why does the loop still turn? (b) The same loop is now held near the end of a bar magnet, where the field is not uniform. Why does it also move bodily? (c) In which position can the loop stay at rest in the uniform field, and which of these positions is stable?
A coil of turns, each of area , has a magnetic moment along its normal. In a field , the torque is , with between the normal and the field. The energy is . An orbiting electron has and .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Part (a). The forces on two opposite sides are equal and opposite, so the net force is zero. But the two forces act along different lines. They make a couple, and a couple gives a torque of size . A torque turns the loop without moving its centre.
Step 2. Part (b). Near a magnet the field is stronger at one side of the loop than at the other. The forces on the two sides are then not equal. They no longer cancel, so there is a net force as well as a torque. The loop moves bodily towards the stronger field when its moment points along the field.
Step 3. Part (c). The torque is zero when or , that is, when the moment points along the field or against it. The first position is stable. A small push brings the loop back. The second is unstable. A small push sends the loop away.
Answer: a couple, a net force from the non-uniform field, and (stable) or (unstable).
Watch out. Zero net force does not mean zero torque.
Log in to join the discussion.
Loading…