3) A wire carrying a current I is oriented in a vertical direction. To its side is a wire loop oriented so that it and the straight wire lie in the same vertical plane. The straight wire is moved toward the loop. If a current is induced in the loop, what is its direction, and what is the direction of the force on the loop? PLEASE EXPLAIN VERY CAREFULLY YOUR ANSWERS.

**fig**

The magnetic field produced by the straight wire is pointing into the page when it passes through the loop. Moving the wire closer to the loop therefore increases the flux into the page. This induces a current in the loop that moves counterclockwise (because such a current produces a magnetic field pointing out of the page inside the loop - Lenz's law). Remember that the field produced by the straight wire is pointing into the page in the plane of the loop. Using the right hand rule to find the direction of the force of the magnetic field on the induced current, we find that the force is always pointing radially inward toward the center of the loop. Since the magnetic field produced by the straight wire is greater for distances closer to the straight wire, the forces to the left of the loop are greater than those to the right. There is therefore a net force pushing the loop to the right.

) When an electron orbits a proton, the smallest circular orbit is one with a radius of about , the Bohr radius. (a) The proton's electric field must have what magnitude to make the electron follow this orbit? (b) Compare the magnitude of the magnetic field that would be required to make an electron move in a circle of the same radius at the speed it would have if it were orbiting a single proton.

a)

b)