Chapter 21

Magnetic Forces and Magnetic Fields

The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) atthe other.

The imaging magnet in most

MRI machines is of the

superconducting type. The

magnet is the most expensive component of the MRI system.

The behavior of magneticpoles is similar to that oflike and unlike electric charges.

Surrounding a magnet there is a magnetic field. The directionof the magnetic field at any point in space is the direction indicatedby the north pole of a small compass needle placed at that point.

The magnetic field lines and pattern of iron filings in the vicinity of abar magnet and the magnetic field lines in the gap of a horseshoe magnet.

When a charge is placed in an electric field, it experiences a force, according to

EFq

The following conditions must be met for a charge to experience a magnetic force when placed in a magnetic field:

1. The charge must be moving.2. The velocity of the charge must have a component that is perpendicular to the direction of the magnetic field.

Right Hand Rule No. 1. Extend the right hand so the fingers pointalong the direction of the magnetic field and the thumb points alongthe velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge.

If the moving charge is negative,the direction of the force is oppositeto that predicted by RHR-1.

DEFINITION OF THE MAGNETIC FIELD

The magnitude of the magnetic field at any point in space is definedas

where the angle (0<θ<180o) is the angle between the velocity ofthe charge and the direction of the magnetic field.

SI Unit of Magnetic Field: T tesla1metercoulomb

secondnewton

Example 1

A proton moves perpendicularly to a magnetic field that has a magnitude of 4.20x10-2 T. What is the speed of the particle if the magnitude of the magnetic force is 2.40x10-14 N?

Example 2

If an electron in an electron beam experiences a downward force of 2.0 × 10−14 N while traveling in a magnetic field of 8.3 × 10−2 T west, what is the direction and magnitude of the velocity?

Example 3

A uniform 1.5 T magnetic field points north. If an electron moves vertically downward (toward the ground) with a speed of 2.5 × 107 m/s through this field, what force (magnitude and direction) will act on it?

Charged particle in an electric field.

Charged particle in a magnetic field.

Does electric force do work on a moving charge?

Does magnetic force do work on a moving charge?

The magnetic force always remainsperpendicular to the velocity and is directed toward the center of the circular path.

Example 1

A 6.0 m wire carries a current of 7.0 A toward the +x direction. A magnetic force of 7.0 × 10−6 N acts on the wire in the −y direction. Find the magnitude and direction of the magnetic field producing the force.

Example 2A wire 1.0 m long experiences a magnetic force of 0.50 N due to a perpendicular uniform magnetic field. If the wire carries a current of 10.0 A, what is the magnitude of the magnetic field?

Example 3

The magnetic force on a straight 0.15 m segment of wire carrying a cur- rent of 4.5 A is 1.0 N. What is the magnitude of the component of the magnetic field that is perpendicular to the wire?

Example 4

The magnetic force acting on a wire that is perpendicular to a 1.5 T uniform magnetic field is 4.4 N. If the current in the wire is 5.0 A, what is the length of the wire that is inside the magnetic field?