Chapter 33The Magnetic Field

L.A. Bumm

Mid-Term Exam 2Wed (30 Mar) Evening 8-10pm

• Please use the MT2 conflict form on D2L if you absolutely cannot be take the midterm at that time.

• Remember that a late start is OK and preferred—but fill out the form so we will expect you.

• Please get the forms to me by Friday (25 Mar).

Magnetic Force Interactions

This is similar to what we observed for electric forces. Electric Force: Like charges repel opposite charges attract

Magnetic Force: Like poles repel opposite poles attract

Magnetism has no equivalent of charge—always dipole

Magnetic monopoles, if they existed, would be analogous to positive and negative charges. However magnetic monopoles have never been observed, although they are predicted by some theories.

Magnetic Field lines

We draw lines of magnetic field.• Magnetic Field lines:

run from North to South• Always form closed loops

because there is no equivalent of charge

What we call the north pole of a magnet is better termed the north seeking pole

Magnetic Field from a Current Carrying Wire

With current: The compass needles are tangent to a circle around the wire.

Without current: The compass needles simply point north.

The magnetic field B has the properties:• A magnetic field is created at all points in space around a current-carrying wire.• The magnetic field at each point is a vector. It has both a magnitude (magnetic

field strength, B) and direction.• The magnetic field exerts forces on magnetic poles. The force on a north pole is

parallel to B; the force on a south pole is opposite to B.

An electric current creates a magnetic field around the wire.

Right hand rule

Looking at Vectors

Tip of the arrow Tail of the arrow

vector field point out of the page vector field point into of the page

Magnetic Torque on Compass Needle

S

N

It can be helpful to remember that B points from north to south. So the north end of the compass needle will want to point to the south pole of the magnet and vice versa.

Current-Carrying Wire2D view looking along wire with current pointing into the page

compass alignment magnetic field lines magnetic field vectors

3D view showing the magnetic field lines and the magnetic field vectors.

A magnet on a pivot is free to rotate. It is placed in a uniform magnetic field pointing to the right as shown. Which way will it turn? Which way will it point?

N

S

Clicker Question

Biot-Savart Law

02

ˆ

4

q r

r

vB

Fundamentally currents are moving charges

The Biot-Savart Law describes the magnetic field from a moving charge. This is as fundamental an equation as the electric field from a point charge.

SI unit of the magnetic field is the Tesla, abbreviated T.

7 –10 4 10 T m A magnetic: permeability of free space

12 2 1 20 8.85 10 C N m electric: permittivity of free space

Coulombs Law and other electric equations contain the proportionality constant ε0. Magnetic equations contain the proportionality constant μ0.

Biot-Savart Law

02

ˆ

4

q r

r

vB

Fundamentally currents are moving chargesThe Biot-Savart Law describes the magnetic field from a moving charge. This is as fundamental an equation as the electric field from a point charge.

The cross product shows that the magnetic field is mutually perpendicular to the velocity of the charge an the line between the charge and the point in space.

r̂v

The magnitude of B is proportional to q and v and the invers square of r.

Direction of B

The sign of the charge is also important. A moving negative charge produces a B in the opposite direction to a positive charge moving in the same direction.

Magnitude of B

Cross Product Review

C DThe cross product of C into D.

Often we say “The cross product of C into D” to emphasize the order of the cross product because that determines the direction.

sinCD C D

The magnitude of the cross product:|C × D| is proportional to the sine of the angle between the vectors.

The direction of the cross product is always mutually perpendicular to both vectors. Thus perpendicular to the plane containing both vectors. Use the right hand rule to determine the direction, up or down. • Align your fingers in the direction to rotate C into D. • Your thumb points in the direction of the cross product.

Direction of the cross product:

C D D C

Stop here