General Physics 2 Magnetism 1

Field Around Magnet• Use a compass to map the direction of the

magnetic field surrounding a magnet.• White board your results. In particular:

– how does the strength of the field vary with distance from the wire?

– how does the field direction relate to the poles of the magnet?

General Physics 2 Magnetism 2

Activity: Map Field of Magnets

• Use iron filings to map the field of a– bar magnet

– horseshoe magnet

• White board results– draw field lines.

– how might magnets generate magnetic fields?

General Physics 2 Magnetism 3

Magnetic Field Lines

• direction of magnetic field, B, is parallel to field line

• number of lines per area is proportional to strength of field

•field lines pointfrom N to S•field lines formclosed loops

General Physics 2 Magnetism 4

Magnetism

No magnetic monopoles!

General Physics 2 Magnetism 5

Magnets are similar to Electric Dipoles

General Physics 2 Magnetism 6

Ferromagnetism

• Ferromagnetic material – iron or other materials that can be

made into magnets

• You can make a magnet from iron by placing it in a strong B field– individual domains become

aligned with external B field

• Loss of magnetism from:– dropping

– heating• Curie temperature

– 1043 K for iron

Random Preferentiallydownwards

General Physics 2 Magnetism 7

Cross Product – Right Hand Rule

General Physics 2 Magnetism 8

Specifying 3 Dimensions

• out of page• tip of arrow

• into page• tail of arrow

General Physics 2 Magnetism 9

Force on a moving charge

• Right Hand Rule (#2)– qv = fingers– B = bend fingers– F = thumb

• Find the direction of the force on a negative charge for each diagram shown.

General Physics 2 Magnetism 10

General Physics 2 Magnetism 11

Think-Pair-Share

• Derive an expression for the radius of an e-’s orbit in a uniform B field. Express your answer in terms of me, v, qe, and B. Turn in your solution!

General Physics 2 Magnetism 12

Earth’s Magnetic Field

• magnetic declination– angular difference

between geographic north and magnetic north

– varies with latitude

Tactics: Right-hand rule for fields

The Source of the Magnetic Field: Moving Charges

The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law:

where r is the distance from the charge and θ is the angle between v and r. The Biot-Savart law can be written in terms of the cross product as

EXAMPLE 33.1 The magnetic field of a proton

QUESTION:

EXAMPLE 33.1 The magnetic field of a proton

EXAMPLE 33.1 The magnetic field of a proton

EXAMPLE 33.1 The magnetic field of a proton

The Magnetic Field of a Current

The magnetic field of a long, straight wire carrying current I, at a distance d from the wire is

The magnetic field at the center of a coil of N turns and radius R, carrying a current I is

EXAMPLE 33.4 The magnetic field strength near a heater wire

QUESTION:

EXAMPLE 33.4 The magnetic field strength near a heater wire

General Physics 2 Magnetism 24

Practice Problems

• Magnetism: Worksheets 1 and 2

• Finish before next class

Tactics: Finding the magnetic field direction of a current loop

Magnetic DipolesThe magnetic dipole moment of a current loop enclosing an area A is defined as

The SI units of the magnetic dipole moment are A m2. The on-axis field of a magnetic dipole is

EXAMPLE 33.7 The field of a magnetic dipole

QUESTIONS:

EXAMPLE 33.7 The field of a magnetic dipole

Tactics: Evaluating line integrals

Ampère’s law

Whenever total current Ithrough passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère’s law:

The strength of the uniform magnetic field inside a solenoid is

where n = N/l is the number of turns per unit length.

The Magnetic Force on a Moving Charge

The magnetic force on a charge q as it moves through a magnetic field B with velocity v is

where α is the angle between v and B.

Magnetic Forces on Current-Carrying Wires

Consider a segment of wire of length l carrying current I in the direction of the vector l. The wire exists in a constant magnetic field B. The magnetic force on the wire is

where α is the angle between the direction of the current and the magnetic field.

EXAMPLE 33.13 Magnetic Levitation

QUESTION:

EXAMPLE 33.13 Magnetic Levitation

General Principles

General Principles

General Principles

Applications

Applications

Applications

Does the compass needle rotate clockwise (cw), counterclockwise (ccw) or not at all?

A. ClockwiseB. CounterclockwiseC. Not at all

A. ClockwiseB. CounterclockwiseC. Not at all

Does the compass needle rotate clockwise (cw), counterclockwise (ccw) or not at all?

The magnetic field at the position P points

A. Into the page.B. Up.C. Down.D. Out of the page.

A. Into the page.B. Up.C. Down.D. Out of the page.

The magnetic field at the position P points

The positive charge is moving straight out of the page. What is the direction of the magnetic field at the position of the dot?

A. LeftB. RightC. DownD. Up

A. LeftB. RightC. DownD. Up

The positive charge is moving straight out of the page. What is the direction of the magnetic field at the position of the dot?

What is the current direction in this loop? And which side of the loop is the north pole?

A. Current counterclockwise, north pole on bottomB. Current clockwise; north pole on bottomC. Current counterclockwise, north pole on topD. Current clockwise; north pole on top

A. Current counterclockwise, north pole on bottomB. Current clockwise; north pole on bottomC. Current counterclockwise, north pole on topD. Current clockwise; north pole on top

What is the current direction in this loop? And which side of the loop is the north pole?

A. LeftB. Into the pageC. Out of the pageD. UpE. Down

An electron moves perpendicular to a magnetic field. What is the direction of ?

B��������������

A. LeftB. Into the pageC. Out of the pageD. UpE. Down

B��������������An electron moves perpendicular to a

magnetic field. What is the direction of ?

What is the current direction in the loop?

A. Out of the page at the top of the loop, into the page at the bottom.

B. Out of the page at the bottom of the loop, into the page at the top.

A. Out of the page at the top of the loop, into the page at the bottom.

B. Out of the page at the bottom of the loop, into the page at the top.

What is the current direction in the loop?

Which magnet or magnets produced this induced magnetic dipole?

A. a or dB. a or cC. b or dD. b or cE. any of a, b, c or d

A. a or dB. a or cC. b or dD. b or cE. any of a, b, c or d

Which magnet or magnets produced this induced magnetic dipole?