The rectangular loop of wire is being moved to the right at constant velocity. A constant current I flows in the long wire in the direction shown. What are the directions of the magnetic forces on the left-hand (L) and right-hand (R) sides of the loop?

The magnetic field around a long straight wire carrying a current is circular, with the direction given by the right-hand rule: if you point your right thumb in the direction of the current, your fingers will curl in the direction of the magnetic field.

In this case, the current in the long wire is flowing upwards, so the magnetic field at the location of the left-hand side of the loop (L) is directed into the page, and at the location of the right-hand side of the loop (R) is directed out of the page.

The force on a current-carrying wire in a magnetic field is given by the Lorentz force law: F = I * L x B, where I is the current, L is the length of the wire, and B is the magnetic field. The direction of the force is given by the right-hand rule: if you point your fingers in the direction of the current and curl them towards the direction of the magnetic field, your thumb will point in the direction of the force.

Assuming the current in the loop is flowing clockwise (since the direction is not specified), the force on the left-hand side of the loop (L) is directed downwards, and the force on the right-hand side of the loop (R) is directed upwards.

So, the directions of the magnetic forces on the left-hand (L) and right-hand (R) sides of the loop are downwards and upwards, respectively.