104494 Physics 108 Equations Sheet

29.2Calculating the Magnetic Field Due to a Current The magnitude of the emf induced in a conducting loop is equal to the rate at which the magnetic flux FB through that loop changes with time.

30-4 Lenz’s Law An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.

30-5 Induction and Energy Transfers

29.3Force Between Two Parallel Currents

30-6 Induced Electric Fields A changing magnetic field produces an electric field.

To find the force on a current-carrying wire due to a second current-carrying wire, first find the field due to the second wire at the site of the first wire. Then find the force on the first wire due to that field. Parallel currents attract each other, and antiparallel currents repel each other.

Electric potential has meaning only for electric fields that are produced by static charges; it has no meaning for electric fields that are produced by induction.

29.4Ampere’s Law

If i and f are at the same point,

30-7 Inductors and Inductance Curl your right hand around the Amperian loop, with the fingers pointing in the direction of integration. A current through the loop in the general direction of your outstretched thumb is assigned a plus sign, and a current generally in the opposite direction is assigned a minus sign.

Solenoid:

30-8 Self-Induction An induced emf is changing.

L

appears in any coil in which the current

30-9 RL Circuits Initially, an inductor acts to oppose changes in the current through it. A long time later, it acts like ordinary connecting wire.

29.5Solenoids and Toroids

29.6A Current-Carrying Coil as a Magnetic Dipole

30-2 Two Experiments 1. A current appears only if there is relative motion between the loop and the magnet (one must move relative to the other); the current disappears when the relative motion between them ceases. 2. Faster motion produces a greater current. 3. If moving the magnet's north pole toward the loop causes, say, clockwise current, then moving the north pole away causes counterclockwise current. Moving the south pole toward or away from the loop also causes currents, but in the reversed directions.

30-3 Faraday’s Law An emf is induced in the loop at the left in Figure 30-1 and Figure 30-2 when the number of magnetic field lines that pass through the loop is changing.