Magnetism

● An electric charge experiences a magnetic force when moving in magnetic field. ● A moving charge produces magnetic field

There are two basic ideas in our introductory study of magnetism.

FIRST THINGS FIRST: THEIR MAJESTY THEMSELVES - MAGNETS

The ancient Greeks, originally those near the city of Magnesia, and also the early Chinese knew about strange and rare stones (possibly chunks of iron ore struck by

lightning) with the power to attract iron. A steel needle stroked with such a "lodestone" became "magnetic" as well, and around 1000 the Chinese found that

such a needle, when freely suspended, pointed north-south - compass.

    The magnetic compass soon spread to Europe. Columbus used it when he crossed the Atlantic ocean, noting not only that the needle deviated slightly from

exact north (as indicated by the stars) but also that the deviation changed during the voyage. Around 1600 William Gilbert, physician to Queen Elizabeth I of England, proposed an explanation: the Earth itself was a giant magnet, with its magnetic

poles some distance away from its geographic ones (i.e. near the points defining the axis around which the Earth turns).

http://www-spof.gsfc.nasa.gov/Education/Imagnet.html

Experience: compass needle rotating in the Earth’s magnetic field

Facts: every magnet, regardless of its shape, has two poles, called north pole and south pole, which exert forces on each other in a manner analogous to electrical charges. The force between like poles is repulsive, and the force between opposite poles is attractive.

Magnets are Cool! North Pole and South Pole

Unlikes Attract Likes Repel

N

S

S

N

N

S

N

S

Contrary to the electric dipole, which we can pull apart and isolate + and – charge, we can NEVER pull apart magnetic dipole. When we cut magnet in two we end up with two smaller dipoles. If we keep on cutting, more magnets will be produced, EACH with north and south pole.

Let’s Break A Magnet!

NS

S SN N

S NS N S NS N

Magnetic monopoles have never been detected.

magnetically-levitated trains…

http://www.scicymru.info/sciwales/indexphpsectionchoose_scienceuser_typePupilpage_id11696languageEnglish.htm

Earth’s A Magnet!The poles received their names because of the behavior of a magnet in the presence of the Earth’s magnetic field. The pole of a magnetic needle that points to the north of the Earth is called north pole. So, magnetic pole which is in the geographic north is magnetically south pole.

Earth's magnetic field has flipped many times over the last billion years.

Don’t freak out:

NS

NS

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)

The Magnetic Field

The direction of the magnetic field at any location is the direction in which the north pole of the compass needle points at that location.

We’ll give definition of mag. field intensity B soon. You can peek – couple of slides later.

A magnetic field is said to exist at a point if a compassneedle placed there experiences a force.

Field Lines of Bar Magnet

Magnetic field lines don’t start or stop.

There are no magnetic charges (monopoles)

But don’t be confused if you see pictures on the right

Magnetic Field Lines

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

Question

Which diagram shows the correct field lines of a bar magnet?

(1) (2) (3)

Field lines do NOT stop abruptly

Field lines are continuous

Convention for direction:

x x x x x x x INTO Page

••••••••••••• OUT of Page

The strength/magnitude of mag. field at any point we define in terms of the force exerted on a charged particle moving with a velocity v

F = qvB sin q

F plane of v and B

The Magnetic Field – strength and direction

A charged particle moving in a magnetic field experiences a (magnetic) force that is perpendicular to the particle’s velocity and, surprisingly, to the magnetic field itself.

Lorentz Force Law, named after the Dutch physicist of the late 19th and early 20th century Hendrik Antoon Lorentz.

The magnitude of the magnetic force on a moving, charged particle is

(q is the angle between the charge’s velocity and the magnetic field)

charge q moving with velocity v in the mag. field B

v

B

q

The direction of the magnetic force is given by the Right-Hand Rule One – RHR 1

► Point fingers in v (or I) directionFpositive charge

F negative charge

► Curle fingers as if rotating vector v (current I) into B.

► Thumb is in the direction of the force.

● For negative charge force is in the opposite direction

F = qvB sin q

F is perpendicular to the plane of v and B

The electric force: Felec = Eq The magnetic force: Fmag = qvB sin q

Charge q in elec. field E and mag. field B

is always parallel to the direction of the electric field. acts on a charged particle independent of the particle’s velocity. does the work when moving charge: The work, W = Fel d cosθ1, is converted into kinetic energy which is, in the case of conductors, transferred to thermal energy through collisions with the lattice ions causing increased amplitude of vibrations seen as rise in temperature.

is always perpendicular to the direction of the magnetic field acts on a charged particle only when the particle is in motion (F=0 if v=0), and only if v and B do not point in the same or opposite direction (sin 00 = sin 1800 = 0). Force is perpendicular to the direction of the motion, so the work done by magnetic force is zero. W = Fmagd cosq1 = 0 (cos 900 = 0). W = ΔKE = 0 Hence change in kinetic energy of the charge is 0, and that means that mag. force can not change the speed of the charge. Magnetic force can only change direction of the velocity, but it doesn’t change the speed of the particle.

In the presence of magnetic field, the moving charged particle is deflected (dotted lines)

Bvv F

FCLICK

θ1 is angle between F and direction of motion (v and d)

We define the magnitude of the magnetic field by measuring the force on a moving charge:

v

Bq

sinqv

FB

The SI unit of magnetic field is the Tesla (T), named after Nikola Tesla,

a Croatian physicist.

mC

sN

sm

C

N

1 T = 1 N·s/(C·m)

Question?

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

Which particle experiences the greatest magnetic force?

1 2 3 Same B

1

2

3F = q v B sin q

Question?

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

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

1) True2) False B

1

2

3

B(fingers) points right.

Velocity points in two different directions.

RHR determines force direction - different!

F = q v B sin q

Two important applications of the Lorentz force are

1) the trajectory of a charged particle in a uniform magnetic field and

2) the force on a current-carrying conductor.

Examples of the Lorentz Force

Motion of charge q in B Fields

qB

mvR

Centripetal force: Fc = mac = m v2/R

in this case Fc is mag. force, so

qvB = m v2/R sin θ = 1

positive charge Force is perpendicular to B,v

B does no work! (W = F d cos θ1 ) Speed is constant (W = Δ KE ) 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

http://www.sr.bham.ac.uk/xmm/fmc4.html

massive or fast charges – large circles

large charges and/or large B – small circles

R

Fv

F

F

F F

F

Question

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.

43

Magnetic force is always perpendicular to velocity, so it changes direction, not speed of particle.

Question

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.

Larger B, greater force, smaller R

qBmv

R

Question

A second particle with mass 2m enters the chamber and follows the same path as the particle with mass m and charge q=25 mC. What is its charge?

1) Q = 12.5 mC

2) Q = 25 mC

3) Q = 50 mC

1 2

v = 75 m/sq = ?? 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.

qBmv

R

If both mass and charge double there is no change in R

2) Suppose that we have a piece of wire carrying charges (again, we'll assume it's positive charges moving around). A number of charges, Dq, moves a distance L in some duration of time, Dt. The force acting on these charges is:

sin sin sinqLF qvB q B LB

t t

F = ILB sinq

This new form of Lorentz law we call the MACROSCOPIC FORM of Lorentz Force Law. We don't have to go down to the microscopic level and look at individual charges and look at their individual speeds. All we have to do is look at a wire, determine its length and the current it carries and we can tell the magnetic force acting on that piece of wire!

Direction of the force:

Put your RIGHT hand fingers in the direction of the conventional current. Curl them towards the direction of the magnetic field. Your thumb will point in the direction of magnetic force.

What is the direction of the force on section a-b?

force is zero

out of the page

into the page

Here = 0.

A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides ab and cd.

B

Question

What is the direction of the force on section b-c of the wire?

force is zero

out of the page

into the page

Force on c-d is Zero!

Force on a-d:out of the page.

I

d c

a b

Net force on loop is

zero

out of the page

into the page

Look from here

a b

cd

F

F

I

d c

a b

•F X

F

Will the loop move?

Yes

NoBut the torque is not zero!

ROTATION

A MOVING CHARGE PRODUCES A MAGNETIC FIELD

1820’s: Hans Oerstad discovers electromagnetism with his famous “compass and current - carrying wire” experiments (by accident)

Currents Create B fields - Ampere’s Law

r = distance from wire

B

0I2r

Magnitude:

Lines of B

rB Current I OUT

Direction: RHR 2

Thumb in direction of current, fingers curl around current indicating direction of magnetic field

B decreases as 1r

m0 = 4p 10-7 Tm/A

x x x x

x x x x

x x x x

x x x x

x x x x

● ● ● ●

● ● ● ●

● ● ● ●

● ● ● ●

● ● ● ●

I

x x x

x x x

x x x

x x x

x x x

● ● ●

● ● ●

● ● ●

● ● ●

● ● ●

I

B decreases as

so the right way that indicates the weaker magnetic field away from

current is this.

BUT!!!! we don’t do it, except when we draw couple of circles.

1r

When indicating direction of B by crosses and dots we always

draw it like this.

Many factories use industrial robots to carry materials or parts around. One type of robot follows a current-

carrying cable buried in the floor by using special sensors to detect the magnetic field around the cable.

v

•B

B

0I2 r

same

v and B are normal in both cases: sinθ= 1

A long straight wire is carrying current from left to right. Near the wire is a charge q (-) with velocity v

I

va)

r

q•

Compare magnetic force on q in (a) vs. (b)

a) has the larger force b) has the larger force c) force is the same for (a) and (b)

q•

r

b)

FF

F has different directions

same F = qvB

Example: A long straight wire carrying a current of I = 3.0 A.

A particle of charge q = 6.5 mC is moving parallel to the wire at a distance of r = 0.050 m from it; the speed of the particle is v = 280 m/s.

Determine the magnitude and direction of the magnetic force exerted on the moving charge by the current in the wire.

► A charge moving through this magnetic field experiences a magnetic force: F = qvB sinq

► Current generates a magnetic field in the space around the wire.

0

2I

Br

( = 90q 0)0

2I

F qvr

F = 2.2x10-8 N

direction: predicted by RHR-1- radially inward toward the wire:

Two long wires carry opposite currents I

What is the direction of the magnetic field above, and midway between the two wires carrying current?

●

Adding Magnetic Fields

1) Left 2) Right 3) Up 4) Down 5) Zero

B

xI I

Example:

Two current-carrying wires exert magnetic forces on one anotherWe already saw that if we put a current carrying wire into a magnetic field it will feel a force....so what will happen when we put two current carrying wires together!?!?! One will create magnetic field that the other will feel a force from, and vice versa! Let us see what is going on.

Force between wires carrying current

I up

B

another I up

F Conclusion: Currents in same direction attract!

x

► Point fingers in v (or I) direction

► Curle fingers as if rotating vector v (current I) into B. ► Thumb is in the direction of the force.

F

I up

B

another I down

F Conclusion: Currents in opposite direction repel!

x

► Point fingers in v (or I) direction

► Curle fingers as if rotating vector v (current I) into B.

► Thumb is in the direction of the force.

F

0 1

0 12 2

0 1 2

2

2

2Force per unit length,

IB

dI

F BI L I Ld

I IFL d

What is the direction of the force on the top wire, due to the two below?

1) Left 2) Right 3) Up 4) Down 5) Zero

What is the direction of the force on the midlle wire, due to the two

others?

1) Left 2) Right 3) Up

4) Down 5) Zero

I I I

What is the direction of the force on the left, due to the two others?

I I I

1) Left 2) Right 3) Up

4) Down 5) Zero

Other way: 1. find magnetic field due the other two and then use RHR1

What is the direction of the force on the midlle wire, due to the two

others?

1) Left 2) Right 3) Up

4) Down 5) Zero

I 2I 3I

What is the direction of the force on the midlle wire, due to the two

others?

I I I

1) Left 2) Right 3) Up

4) Down 5) Zero

What is the direction of the magnetic field produced in the

midlle between two wires?

1) Left 2) Right 3) Up

4) Down 5) Zero

I I I

What is the direction of the force on the left, due to the two others?

I I I

1) Left 2) Right 3) Up

4) Down 5) Zero

Other way: 1. find magnetic field due the other two and then use RHR1

Electric and Magnetic Field

Direction:

Opposites Charges Attract Currents Repel

Electric MagneticSource: Charges Moving ChargesAct on: Charges Moving ChargesMagnitude: F = q E F = q v B sin θDirection: Parallel to E Perpendicular to v,B

SolenoidsA solenoid consists of several current loops stacked together.

In the limit of a very long solenoid, the magnetic field inside is very uniform:

B=m0nIn = number of windings per unit length,I = current in windings

B 0 outside windings

Example Problem 1

A solenoid that is 75 cm long produces a magnetic field of 1.3 T within its core when it carries a current of 8.4 A. How many turns of wire are contained in this solenoid?