BoardWork

Indicate which pole of the magnet is north and which is south. (The blue lines represent magnetic field lines.)

Magnets and Currents

interacting and inseparable

Objectives

• Describe the magnetic field caused by an electrical current.

• Determine the force on an electric charge in a magnetic field.

What’s the Point?

• What is the force that underlies electric motors?

Current Creates Magnetism

An electric current creates a magnetic field.

Look, Ma! No poles!

Vector Direction Conventions

Up Down

In Out

RightLeft

Poll Question

If a wire in front of you carries a current from left to right, what is the direction of the resulting magnetic field where you are?

I

A. B. C.

D. E. F.

Board Work

An electric current creates a magnetic field whose lines circle right-handed around it. Draw lines for the magnetic field created by a ring of current.

I

Magnetic Field of Current Ring

Source: Griffith, The Physics of Everyday Phenomena

N

S

dipole field

Solenoid Magnetic Field

Source: Griffith, The Physics of Everyday Phenomena

N S

Electrons are Magnets!

spin

Electrons are Magnets!

current

Electrons are Magnets!

magnetic field

Electrons are Magnets!

N

S

magnetic dipole

Types of Magnets

• Electromagnets– currents travel through conducting coils

• Permanent Magnets– materials whose electrons have aligned spins

or orbits

Moving charges create the fields!

The Lorentz Force

making electrons work for us

Magnetic Force on a Charge

• Currents create magnetic fields.

• Currents are made of moving charges.

• Moving charges are magnets.

• Magnets apply forces to each other.

• Magnets apply forces to moving charges.

How do those forces behave?

Lorentz Force

Right-Hand Rule

F = qv B

Source: Griffith, The Physics of Everyday Phenomena

qv

Poll Question

What is the direction of the cross product A  B?

A

B

A.

B.

C.

D.

E.

F.

Cross Product Review

A

B

a

b

AB = area of parallelogram

Cross Product Review

• Curl right-hand fingers in direction of

• Right-hand thumb points in direction of cross-product

• Not commutative

A

B

a

b

AB = –(BA)

Lorentz Force Properties

• F = 0 unless charge is moving

• F = 0 if velocity is to field

• F = maximum if velocity is to field

• F 0 only if charge crosses B field lines

• If q, v or B reverse, direction of F reverses

paper square

Make an Origami Right Hand

fold over

magnetic

fieldcurrent

qv

For

ce

Lore

ntz

vectors

creases:in out

Think Question

What is the direction of the force on the object moving with velocity v through magnetic field B?

B

v

+

A.

B.

C.

D.

E.

F.

B

Group Poll Question

What is the magnitude of the force on object A compared to the magnitude of the force on object B?

v

q

v

2qA BA. FB = 4 FA

B. FB = 2 FA

C. FB = FA

D. FB = FA/2

E. FB = FA/4

B

Group Poll Question

How does the work done on object A compare to the work done on object B?

v

q

v

2qA B

A. wB > wA.

B. wB = wA.

C. wB < wA.

Lorentz and Newton’s third law

• F = qv B does not explicitly include a reaction force.

• Magnetic fields (B) are always created by moving charges.

• Moving charges (qv) always create magnetic fields.

• The moving charge creating B “feels” the field of qv. So F = qv B goes both ways.

Here’s where it is:

Board Work

From F = qv × B, find the SI unit of magnetic field B.

Challenge Question

A current runs through one wire of a pair of parallel wires. What is the direction of the resulting magnetic field at the location of the other wire?

I

??

Force between parallel currents

What is the force on this current?I  B

Definition of Ampere

• If two parallel wires are held 1 m apart,

• with currents of 1 A through each wire,

• the attractive force between the wires is 2  10–7 N for each meter of length of the wires.

Reading for Next Time

• Faraday’s law

• Big Ideas– A changing magnetic field can create an

electric potential– AC Transformers can be understood using

Faraday’s law and conservation of energy

• Very abstract– You are ready– It is very cool