Chap 21 & 22: Magnets & Magnetic Fields

objectives

• Did this– Charges

– Force between charges & Electric Field

– Moving charges, current

• will do this– Magnetic Field

– Force on moving charges in magnetic field

– Generation of magnetic field by moving charges

– Generation of current by moving magnetic field

Examples of Magnets

• Compass• Earth• Hi-Fi speakers• Fridge magnets• Electric motors• Scrap yards• Cupboard doors

• video/audio tapes

Properties of magnets

As with charges we find that there are attractive and repulsive forces.

We find that magnets stick to certain non-magnetised materials

We find that magnets can both attract and repel each other

EARTH’S MAGNETIC FIELD

Aurora Movie

Magnetic Induction

Ferromagnetic materials such as iron, cobalt, gadolinium and dysprosium can become permanently magnetic

Paramagnetic materials such as steel can become magnetised but this will only last for a short time

Magnetism can be induced in materials by rubbing with another magnetised material

Magnetic Induction

A permanent magnetised ferromagnet can thus be attracted to paramagnetic material by inducing magnetism in that material

Magnets are Cool!

NS

+-

• North Pole and South Pole– Opposites Attract– Likes Repel

Lets Break it!

• Magnetic Field Lines– Arrows give direction – Density gives strength– Looks like dipole!

Permanent Magnets

• North Pole and South Pole– Opposites Attract– Likes Repel

• Magnetic Field Lines– Arrows give direction – Density gives strength– Looks like dipole!

NS

NS NS

Lets Break it!

Field Lines of Bar Magnet

S N

Complete the lines

Magnetic Poles

In electrostatics there are two types of charges: positive and negative

Similarly there are two types of “poles”:North and South

The North pole of a compass needle points to the geographical north pole.

Like poles repel Dislike poles attract

By convention:

Quick Quiz

The Geographical North pole is defined where the axis of rotation of the earth goes through the arctic

North

Is this:

• Exactly the north magnetic pole

• Nearly the north magnetic pole

• Exactly the south magnetic pole

• Nearly the south magnetic pole

MonopolesUnlike with electric charge no isolated magnetic pole or monopole has ever been discovered

A north pole is always found with a corresponding south pole

No Magnetic Charges

• Magnetic Fields are created by moving electric charge!

• Where is the moving charge?

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)

Magnetic Field

Magnetic Field like the Electric Field is another example of a vector field

It is defined everywhere

It has a magnitude Units: 1ms C

N Tesla (T)

It has a direction, the direction that a compass needle would point

Magnetic Field Lines

If we move a compass around and record the direction it points everywhere we can map out the direction of the magnetic field lines

Magnetic Field Lines

Magnetic Field Lines

Experiments of Pierre de Maricourt mapped out the field lines on naturally magnetic sphere

Demonstrated that they all pointed to two diametrically opposed points or “poles”.

Moving charges in a magnetic field

Moving charges in a magnetic field experience a magnetic force

Magnetic Field

N S

NS

B

Magnetic Field, B, is in direction compass needle points Magnitude is defined in terms

of force on moving charges

Moving charge in magnetic field

Experiments show

FB

v

+

B

B

B

Electric vs Magnetic Field Lines

• Similarities– Density gives strength– Arrow gives direction

• Leave +, North

• Enter -, South

• Differences– Start/Stop on electric charge– No Magnetic Charge, lines are continuous!

Difference betweenElectric & Magnetic Forces• acts in the direction of

the electric field • acts on a charged

particle regardless of whether the particle is moving

• does work in displacing the particle

• acts perpendicular to the magnetic field

• acts on a charged particle only when the particle is moving

• does no work in displacing the particle

Force on a moving charge

BvF qB

BvF qB

The result of all of these experiments can be summarised by this equation

We can use this relationship to define the magnitude of B

Units: 1ms C

N Tesla (T)

Work & Energy

Magnetic force does no work in

displacing a moving particle Kinetic energy

of particle cannotchange

speed cannot changebut velocity and

direction can

Charged particle in uniform magnetic field

Magnetic field into boardBvF qB

+

v v

FB

+

+

++

+

+Note speed never changes

but direction does

Force is always to v

Charged particle in uniform magnetic field

Magnetic field into board

BvF qB

v

FB

+

+Since force is always radial it acts to keep particle moving in a circle

qvBFB r

mv2

r

mvqB

qB

mvr

Right hand rule

Review RHR• Force on moving (+) charge

in Magnetic field – Thumb….. gives F on + charge– fingers……. I(or v), – palm….. B (field)

•

Palm out of page.

BI

F

+ v+ + +

x

Thumb out, fingers up, palm left.

•Magnetic field produced by moving charge.

–Thumb I, fingers where you want it, palm gives B

Direction of Magnet Force on Moving Charges

Velocity B Force

out of page right

out of page left

out of page top

out of page down

Right Hand Rule• Thumb ___, Fingers ___, palm ___

• Negative charge has opposite F!

Preflight

What is the direction of the magnetic field in region 1?

1) up

2) down

3) left

4) right

5) into page

6) out of page

1 2

v = 75 m/sq = +25 mC

Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.

Force on moving charge in magnetic Field

• The magnitude of the magnetic force FB

exerted on the particle is proportional to the charge q and to the speed of the particle v

• The magnitude and direction of the force FB

depend on the velocity of the particle v and the magnitude and direction of the magnetic field B

Force on moving charge in magnetic Field

• When the particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero

• When the particle’s velocity vector v makes an angle with the magnetic field the magnetic force acts in a direction perpendicular to both v and B i.e. F is to the plane formed by v and B

Force on moving charge in magnetic Field

• The magnetic force exerted on a positive charge is in the opposite direction of the force exerted on a negative charge moving in the same direction

• The magnitude of the magnetic force exerted on the moving particle is proportional to sin where is the angle the particles velocity vector makes with the direction of B

Charged particle in uniform magnetic field

qB

mvr

m

rqBv

m

qB

r

v

rBq

mv

q

p

v

rB

q

m

Bubble chamber

Mass spectrometer

angular velocity

velocity

Direction of Magnet Force on Moving Charges

Velocity B Force

out of page right

out of page left

out of page up

out of page down

Right Hand Rule• Thumb ___, Fingers ___, palm ___

• Negative charge has opposite F!

Preflight

What is the direction of the magnetic field in region 1?

1) up

2) down

3) left

4) right

5) into page

6) out of page

1 2

v = 75 m/sq = +25 mC

Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.

• The magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field.

• F = q v B sin()– Direction from RHR

• Thumb (v), fingers (B), palm (F)

– Note if v is parallel to B then F=0

BV

Magnitude of Magnet Force on Moving Charges

Example

The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field.

1) Which particle experiences the greatest magnetic force?

1) 1 2) 2 3) 3 4) All Same

2) The force on particle 3 is in the same direction as the force on particle 1.

1) True 2) False B

1

2

3

Electric vs Magnetic

Electric MagneticSource: Charges Moving ChargesAct on: Charges Moving ChargesMagnitude: F=Eq F = q v B sin()Direction: Parallel E Perpendicular to v,B

Velocity SelectorDetermine magnitude and direction of

magnetic field such that a positively charged particle with initial velocity v travels straight through and exits the other side.

v

Ex x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x x

What do you need to change if want to select particles with a negative charge?

Motion of q in uniform B field

• Force is perpendicular to B,v– B does no work! (W=F d cos )– Speed is constant (W= K.E.)– Circular motion

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

x x x x x x x

Uniform B into page

v F• Force is perpendicular to B,v

• Calculate R

R

Preflight

What is the speed of the particle in chamber 2.

1) v2 < v1

2) v2 = v1

3) v2 > v1

1 2

v = 75 m/sq = +25 mC

Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1=75 m/s up, and follows the dashed trajectory.

Preflight

Compare the magnitude of the magnetic field in chambers 1 and 2

1) B1 > B2

2) B1 = B2.

3) B1 < B2

1 2

v = 75 m/sq = +25 mC

Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.

Magnitude of Field inside of solenoid : B=0 n I

n is the number of turns of wire/meter on solenoid.

Solenoids

Direction Thumb direction of I, fingers point toward center, palm gives direction of B.

What is the net force between the two solenoids?

a)Attractive

b) Zero

b)Repulsive

Look at field lines, opposites attract.

Look at currents, same direction attract.