AP Physics C III.D – Magnetic Forces and Fields

The source and direction of magnetic fields

The magnitude and direction of the magnetic force on a moving charge in a magnetic field

Contrasting electric forces and magnetic forces

Motion of a charge particle in a magnetic field

The radius of a charged particle in a magnetic field

Ex. A particle with charge +q traveling with velocity v, enters a uniform magnetic field B, as shown below. Describe the subsequent motion of the particle. B +q+q v

The magnetic force on a current carrying wire

Ex. A U-shaped wire of mass m is lowered into a magnetic field B that points out of the page. How much current I must pass through the wire such that the net force on the wire is zero?

Ex. A rectangular loop of wire that carries current I is placed in a uniform magnetic field B as shown below. What is the net torque on the loop?

Ex. The middle portion of the wire below is bent into the shape of a semicircle of radius r. The wire carries a current I. What is the total magnetic force that acts on the wire in the field, B?

The tangent galvanometer and RHR-2

+e v0v0

Forces between two current carrying wires

Ex. Two long, parallel wires are separated by distance r. If currents I 1 and I 2 are established in the wires, and the currents are in the same direction, what is the magnetic force per unit length the wires exert on each other?

Ex. Use the Biot-Savart Law to find the magnetic field of the wire at point P.

Ex. Find the magnetic field at the center of a current carrying semi-circular loop with radius r.

Ex. A long coaxial cable that is composed of a solid cylindrical conductor of radius R 1, surrounded by a thin conducting cylindrical shell of radius R 2. The inner cylinder carries a current of I 1 and the outer cylindrical shell carries a smaller current of I 2 in the opposite direction of I 1. Use Ampere’s Law to find the magnitude of the magnetic field a) in the space between inner cylinder and the shell and b) outside the shell.

The magnetic field of a solenoid. We can derive this one so here goes...

Ex. A tightly wound solenoid has a length of 30 cm, a diameter of 2.0 cm and contains a total of turns. If it carries a current of 5.0 A, what is the magnetic field inside the solenoid?

Ex. A toroidal solenoid (a solenoid bent into a doughnut shape) has in inner radius R 1 and outer radius R 2. It consists of N windings and the wire carries current I. What is the magnetic field in each of the following regions? a) r R 2

A note on uniform current density.