SAT Physics Subject Test
Chapter 11 Magnetic Forces and Fields
THE MAGNETIC FORCE ON A CURRENT-CARRYING WIRE
Since magnetic fields affect moving charges, they should also affect current-carrying wires. After all, a wire that contains a current contains charges that move.
Let a wire of length l be immersed in magnetic field B. If the wire carries a current I, then the magnitude of the magnetic force it feels is
FB = IℓBsinθ
where θ is the angle between ℓ and B. Here, the direction of ℓ is the direction of the current, I. The direction of FB is given by the right-hand rule as before, remembering that the direction of the current is the direction that positive charges would flow.
5. A U-shaped wire of mass m is lowered into a magnetic field B that points out of the plane of the page. What is the direction of the net magnetic force on the wire?
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The total magnetic force on the wire is equal to the sum of the magnetic forces on each of the three sections of wire. The force on the first section (the right, vertical one), FB1, is directed to the left and the force on the third piece (the left, vertical one), FB3, is directed to the right. Since these pieces are the same length, these two oppositely directed forces have the same magnitude, Iℓ1B = Iℓ3B, and they cancel. So the net magnetic force on the wire is the magnetic force on the middle piece. Since I moves to the left and B is out of the page, FB2 is directed upward.
6. A rectangular loop of wire that carries a current I is placed in a uniform magnetic field, B, as shown in the diagram below. The loop is free to rotate about a vertical axis through its center. Describe the direction in which the loop will rotate.
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Ignoring the tiny gap in the vertical left-hand wire, we have two wires of length ℓ1 and two of length ℓ2. There is no magnetic force on either of the sides of the loop of length ℓ2, because the current in the top side is parallel to B and the current in the bottom side is antiparallel to B. The magnetic force on the right-hand side points out of the plane of the page, while the magnetic force on the left-hand side points into the plane of the page.
If the loop is free to rotate, then each of these two forces exerts a torque that tends to turn the loop in such a way that the right-hand side rises out of the plane of the page and the left-hand side rotates into the page.