1

Circuits revision

• Here’s the circuit for the flashing neon bulb.

• What is the period of the flash in seconds ?

2

Magnetic Fields revision

Please try problem 15 in Ch 24 on page 825.

“What is the magnetic field at the center of the loop….”

3

Magnetic Fields and Forces

• Magnetism

• Magnetic field shapes and direction

• Fields near electric currents

• Magnetic forces

• Moving charges and magnetism

• Magnetic machines

• Magnetic materials

4

Magnetism

• Fundamental force of nature

• Related to electricity, but not the same

5

Experimental Observations

• Magnetism does not move an electroscope, it does not act on stationary charges

• Long range force (action over a distance)

• There are 2 poles, north and south, and they come in pairs

• Like poles repel, unlike poles attract

• Poles attract magnetic materials

6

Magnetic Field lines

• Magnetic Fields around a bar magnet

• Similar to an electric dipole

• Start at north pole, terminate at south pole

7

Like and unlike poles

Magnetic field lines between poles

8

Electric Currents and Magnetic Fields

Oersted found that a current can move a magnetic compass

9

Direction of Magnetic field

We use the right handed rule to find which way a magnetic compass would point

10

Magnetic field near a loop• Bend the wire into a loop.

• Dots - field is coming out of the page.

• Crosses - field is going in to the page

11

Field near a solenoid

• Many loops will concentrate the field inside the coil

• Called a solenoid – contains a uniform magnetic field

12

Magnetic field due to a current

Experimentally, the field strength, B, is proportional to current, I, and inversely proportional to distance, r.

Units of Tesla, where μ0 is the permeability constant – 1.257x10-6 TmA-1

r

IB

2

0

13

Tesla is a large unit

• Magnets in the lab – 0.1 to 1 T

• Kitchen magnets – 5x10-3 T

• Earths magnetic field – 5x10-5 T

• Superconducting magnets – in accelerators and maglev trains – 10 T

14

Magnetic Field at the center of a current loop

Inside a loop radius R:

R

IB

2

0

15

Magnetic Field at the center of a current loop with N turns

If the loop has N turns, but its not yet a solenoid we have:

R

NIB

2

0

16

Magnetic field inside a solenoid

The uniform field in a solenoid is

For a solenoid with N turns, Length L and current I.

Note: independent of the coil radius. Field is uniform.

L

NIB 0

17

Magnetic Forces

• The magnetic fields around two wires will attract or repel, just like bar magnets.

• A magnetic field exerts a force on a current, or moving charge

• Currents in the same direction attract

• Opposite currents repel

18

Direction of Magnetic Force

• The force on a wire with a current is perpendicular to both the magnetic field the direction of the current.

• We use another right hand rule

19

Magnitude of the Magnetic Force

The force between a magnetic field and a current along a wire length L perpendicular to the field is:

ILBF

20

Magnitude of the Magnetic Force

The force between a magnetic field and a current along a wire length L at an angle, α to the field is:

If the current and B field are parallel – there is no force.

sinILBF

21

Force on a moving charge

• A current, I, is a moving charge.

• The charge q moves along the wire length L in time Δt

• The velocity will be L/Δt

• We find that qv=IL qvIL

L

qv

t

qI

t

Lv

22

Magnitude of the Magnetic Force

The force between a magnetic field and a charge, q, moving with a velocity, v perpendicular to the field is:

qvBF

23

Magnitude of the Magnetic Force

The force between a magnetic field and a charge, q, moving at velocity, v, at an angle, α to the field is:

If the moving charge and B field are parallel – there is no force.

sinqvBF

24

Direction of Magnetic Force

• The force on a moving charge is perpendicular to both the magnetic field the direction of the charge.

• Note the thumb is now the direction of the +ve charge, instead of the current I.

25

Path of charges in a magnetic field

• The force on a charged particle in a magnetic field is perpendicular to its direction of motion.

• We always get circular or spiral paths of charged paths in a magnetic field

26

Path of charges in a magnetic field

• Centripetal force of an object in a circle

m

RqBv

qvBr

mvF

2

27

Path of charges in a magnetic field

• If we accelerated the ions in an electric field V, the charge to mass ratio can be measured,

22

2

2

2

1

RB

V

m

q

mvqVE

28

Mass spectrometer

• First measurement of e/m for the electron

• Used to distinguish different types of atoms and isotopes

29

Aurora Borealis

• Solar wind from the sun (protons & electrons) gets deflected by Earth’s magnetic field.

• Portion of velocity perpendicular to the field lines, curves the ionizing particles into spirals

• Ionize O2 and N2 in the ionosphere

30

Magnetic forces between currents

• Consider two wires carrying currents I1 and I2.

• The field at the top wire is

d

ILIF

LIBF

d

IB

2

2

21012

1212

202

31

Magnetic forces between currents

From the field from the single wire, we can deduce the force between 2 wires carrying currents I1 and I2 is

d

ILIF wiresparallel

2

210

32

Torques and Magnetic Moments• Torque was defined in chapter 7

• Quantity to measure the force applied near a pivot

• Useful for calculating rotational motion

33

Torque

Torque, τ, measures the effectiveness of a force at causing an object to rotate about a pivot

sinrF

34

Torque on a current loop in a B field

• Current loop in a uniform field

• The forces on the top and bottom wires will rotate the loop

35

Torque on a current loop in a B field

• The total torque, τ, will be the sum of the torques on the top and bottom wires.

• Loop height L, wire length W

sin

sin2

2

BIWL

LF

36

Torque on a current loop in a B field

•In general, the torque on a loop area A will be:

The loop is forced to align with the magnetic field

sinIAB

37

Using torque - MRIs

• Magnetic Resonance Imaging (MRI) uses the protons magnetic moment in hydrogen atoms in high 1T fields.

• The rate of the emitted radio waves from the excited states are detected

38

Using Torque – Electric motor

Using commutators, the loop can be made to spin, to produce rotational movement

39

Permanent Magnets -Ferromagnetism

• Ferromagnetism is a property of certain elements – the ability to maintain a permanent magnetic field

• Depends on the crystalline structure of the metal

• Found in alloys of iron, cobalt, nickel, gadolinium, dysprosium, europium

• Half full electron shells, the magnetic dipole of the electrons can align

40

Periodic Table

41

Crystalline structure aligned

• The magnetic dipoles are grouped in micron size crystals, domains

• The dipoles can be aligned by applying a magnetic field

• Can be destroyed by heating (Curie point) or dropping

42

Electromagnets

• An iron core near a solenoid will align the domains inside the iron

• This increases the magnetic field (factor of 100)

• Used to amplify the magnetic field

43

Summary

• Magnetism

• Magnetic field shapes and direction

• Fields near electric currents

• Magnetic forces

• Moving charges and magnetism

• Magnetic machines

• Magnetic materials

44

Homework problems

Chapter 24 Problems

20, 21, 31, 41, 48, 53, 56, 57