PHYS 2421 - Fields and Waves

Remember Coulomb’s law:

Magnetism: the idea

q2 feels a force

changing in

magnitude and

direction

This is the origin of magnetism and it is produced by

moving charges and affect only moving charges

Now put q1 in motion

F F q1 q2

r

1 2

2

q qF k

r =

In chapter we will study: • Permanent magnets

• Magnetic fields

• Effect of magnetic fields

• on charges • on currents

• on loops (torque)

PHYS 2421 - Fields and Waves

Background: • 1st record of magnetic iron ore appeared in Magnesia 2500 years ago

• H.C. Ørsted studied relation between electricity and magnetism,

followed by Ampere, Gauss and Faraday.

• Maxwell synthesize his equations combining electricity and

magnetism

• Einstein’s theory of relativity show that electricity is the

same as magnetism in a different frame of reference

• Shen Kuo was the first scientist to use magnetic needles in navigation

A few facts: • Magnets have poles, usually called north or south

• Equal poles repel, unequal poles attract

• Magnets attract some un-magnetized metals

• The earth has a

magnet but its N and

S are opposite to the

geographical north

and south

• There are no single poles

• Ørsted: electric currents deflect compasses like magnets

Remember the electric case

Follow a similar approach for the magnetic case

A few facts: •A moving charge creates a magnetic field

•The magnetic field, B, exerts forces on other moving charges

•The force is given by

where v is the velocity of the moving charge F qv B

sinF q vB •The magnitude is given by

where is the angle between V and B

•The units of the magnetic field are

N N N

TeslaC m/s m C/s Am

FB

qV

Some examples

Homework : Problem 27.1 and 27.7 (11th Ed.) or

27.1 and 27.5 (12th Ed.)

In negative y direction

19 5 0

14

sin

1.6 10 3 10 2 sin 30

4.8 10

C m/s T

N

F qv B F q vB

F

Summary of Section 27.2

Hmwk Section 27.2: Problems 27.1 and 27.7 (11th Ed.) or

27.1 and 27.5 (12th Ed.)

The force produced by a magnetic field B on a

charge q moving at velocity is:

Its magnitude is:

and B is measured in units of:

F qv B

sinF q vB

N

TeslaAm

In electric case E and F are parallel or antiparallel F qE

In the magnetic case B is always perpendicular to F

F qv B

Thus, the magnetic B lines are not “force lines

Some examples of direction of B fields

More examples of direction of B fields

Notice that all B lines close on itself

For closed surfaces, since all B lines close on

itself, the flux will be zero

Now calculate magnetic flux over an area A:

B B A

0B B dA

Magnetic version of Gauss law

Units:

Weber

Wb = T x m2

Homework : Problems 27.11 and 27.12 (11th Ed.) or

27.11 and 27.12 (12th Ed.)

Soln P. 12: a) 0, b) -0.0115Wb, c) b) +0.0115Wb d) 0

0

3

0 4

0.9 106

3 10 0.5

cos60

cos60

B

BB

B A BA

A

2

Wb T

m

Summary of Section 27.3

Hmwk Section 27.3: Problems 27.11 and 27.12 (11th Ed.) or

27.11 and 27.12 (12th Ed.)

B B A 0B B dA

B field lines

Magnetic flux