I have a question about a problem regarding Newton's third law.

Question

a. An iron rod is held up by a magnet. The magnet is held up by a string (from a ceiling, let's say). Draw a free-body diagram for the magnet and a separate free-body diagram for the iron rod.

For the rod I have a gravitational force going downward, and magnetic force pointing upward and a contact force pointing downward.

For the magnet I have a gravitational force pointing downward and a tension force and contact for pointing upward.

Is this correct?

b. For each of the forces drawn, identify the corresponding force that completes the Newton's third law pair.

I know the two contact forces are pairs, but am unclear about the other pairs.

No. THe rod has gravity down, magnetic force up equal to the rods'weight. For the magnet, gravity down equal to rods weight, magnetic force up. THen for the string, magnetic and rod weight down, and tension up equal to that weight.

I don't agree with Bob's answer here. The iron rod is not levitating here (it's theoretically possible, but I don't think that is meant here), so we must assume that it is in contact with the magnet.

"For the rod I have a gravitational force going downward, and magnetic force pointing upward and a contact force pointing downward."

This is correct.

"For the magnet I have a gravitational force pointing downward and a tension force and contact for pointing upward."

Here you forgot the magnetic force exerted by the rod on the magnet. This force is pointing downward.

Besides the tension forces you have the magnetic forces as third law pairs.

If you consider the other forces (the tension force and the gravitational force), you must include the objects in which that force is exerted.

So, the tension force exerted by the sring is on the magnet is opposite to the force exerted by the magnet on the string.

The gravitational force exerted by the Earth on the rod is opposite to the gravitational force exerted by the rod on the entire Earth. Sounds strange but it is true! And the same is true for gravitational force exerted on the magnet.