AP Physics CIII.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

Ex. A charge C moves with a speed of m/s an angle of 30.0° through a magnetic field strength of B = 0.4 T. What is the magnetic force on +q?

Motion of a charge particle in a magnetic field

The radius of a charged particle in a magnetic field

Ex. A particle of charge –q moves through a region that contains an electric field E, crossed with a perpendicular magnetic field B. If N/C and B = 0.5 T, what is the speed of the particle through this region if it is not deflected?

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

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

Magnetic field about a current carrying wire (we have seen this

before and will derive it in a minute)

Ex. The diagram below shows a proton moving with a speed of m/s, initially parallel to and 4.0 cm from a long, straight wire. If the current in the wire is 20 A, what is the magnetic force on the proton?

+ev0

Forces between two current carrying wires

Ex. Two long, parallel wires are separated by distance r. If currents I1 and I2 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?

Biot-Savart Law

This intimidating beast is found experimentally, so fortunately we

don’t have to derive it.

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.

Ampere’s Law (derived, by other people, not us, from the Biot-Savart

Law)

Ex. Use Ampere’s Law to show that the magnetic field due to an infinitely-long straight wire carrying a current I is given by the equation where R is the distance from the wire.

Ex. A long coaxial cable that is composed of a solid cylindrical conductor of radius R1, surrounded by a thin conducting cylindrical shell of radius R2. The inner cylinder carries a current of I1 and the outer cylindrical shell carries a smaller current of I2 in the opposite direction of I1. 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. . .

where in is the number of turns per unit length (N/L)

Ex. A tightly wound solenoid has a length of 30 cm, a diameter of 2.0 cm and contains a total of 10 000 turns. If it carries a current of 5.0 A, what is the magnetic field inside the solenoid?

Ex. A tightly wound solenoid with n coils per unit length has a current I. Use Ampere’s Law to show the magnetic field inside this ideal solenoid is given by the equation .

Ex. A toroidal solenoid (a solenoid bent into a doughnut shape) has in inner radius R1 and outer radius R2. It consists of N windings and the wire carries current I. What is the magnetic field in each of the following regions? a) r < R1 b) R1 < r < R2 and c) r > R2

A note on uniform current density.