The graded exams are being returned today. You will have until the next class on Thursday, Nov 10 to rework the problems you got wrong and receive 50% added credit. Make sure you are in class as you will not have another opportunity to turn in the reworked exam. I will be going over the answers in class on Thursday. This will also be your only opportunity to ask for corrections/clarifications on any grading mistakes.

Magnetic Dipole in a Non-uniform Magnetic Field y

Magnetic Dipoles and How Magnets Work

The Direct-Current Motor

Magnetic Field of a Moving Charge Magnetic field of a point charge moving with constant velocity

Example: Force between two moving protons Find the ratio of electric and magnetic forces on the protons Magnetic field of the lower proton at the position of the top one

Magnetic Field of Current Element The Biot-Savart law.

Magnetic field around a straight wire

Magnetic Field of Two Wires Field at points on the x-axis to the right of point (3) Magnetic field outside of a conductor pair falls off more rapidly

Magnetic field of a circular arc

Magnetic Field of a Circular Current Loop Falls off just as the electric field of the electric dipole Magnetic Field on the Axis of a Coil

The magnetic field of a (small) loop behaves “on the outside” like the electric field of the electric dipole of the same orientation – that’s why “magnetic dipole”.

Magnetic force between two parallel conductors with currents

Example: Two straight, parallel, superconducting wires 4.5 mm apart carry 15,000 A current each in opposite directions Should we carry about the mechanical strength of the wires?

Ampere’s Law

General Statement Magnetic fields add as vectors, currents – as scalars

Just as with the integral form of Gauss’s law, the integral form of Ampere’s law is powerful to use in symmetric situations

Magnetic Field of a Solenoid