Chapter 28: Magnetic Fields

Introduction

What are we going to talk about in chapter 29:

• What are magnetic fields intensity (B)?

• How do we create magnetic fields?

• What are the SI units for B?

• What is a magnetic ‘pole’?

• How do magnetic field lines of a magnet look?

• What is the force on a charged particle due to an electric field.

• What if there is both and electric and a magnetic field affecting a charged particle?

A magnet has a magnetic field.

Anything else gives MF?

28-2 :The Magnetic Field (B):

Currents are sources of magnetic fields (e.g. electromagnet).

What happens to a charged particle when it moves through a magnetic field?

What happens to a computer diskette when brought next to a strong magnet?

28-3: The definition of B:

FB = q v x B

Review the cross product and the right hand rule.

Boldface means vector

[B]: tesla (T) = (N s)/(C m) = N/(A m)

1 T = 10000 gauss

Checkpoint #1

Can the magnetic force change the speed of a particle?

Can the magnetic force change the kinetic energy of a particle?

Can the magnetic force change the velocity of a particle?

Can the magnetic force accelerate a particle?

Can the magnetic force change the momentum of a particle?

The magnetic force is always perpendicular to the velocity and the magnetic field.

Magnetic field lines and magnetic poles:

The idea of field lines is similar to that of the electric field: direction and intensity.

How do lines for a bar magnet look like? ‘north’ pole, ‘south’ pole, flux over closed surface = 0

How do lines for the horseshoe and the C magnets look like?

What happens if we place two magnets close to each other?

Opposite magnetic poles attract; similar poles repel.

How does the magnetic field of earth look like? (the geomagnetic ‘north’ pole)

If E is perpendicular to B, we say they are ‘crossed’.

24-8: Crossed fields:

Explain the J.J. Thompson experiment that led to the discovery of the electron.

With B = 0, by measuring y, and knowing E, JJT realized that the ‘charged’ particles are negatively charged!

With B ≠ 0, there is no deflection when

v = E/B

This is how one can measure the e-/m ratio for electrons!!

Checkpoint #2

But:2

2

2mv

qELy

Therefore:yE

LB

q

m

2

22

Interaction:

Prove it

q v B = mv2/r

28-6: A circulating charged particle:

If a charged particle is moving in a plane perpendicular to a magnetic field, then:

r = mv/qB

T = 2 m/(qB)

f = qB/(2 m)

Radius of circular motion:

Period for one rotation:

Frequency of rotation:

Checkpoint #4

Angular frequency of circular motion:

The nice thing is that T, f and are independent of v!!

= qB/m

Applications:• velocity selector• mass spectrometry• cyclotron accelerators

Helical paths

What happens if the velocity is not perpendicular to the magnetic field?

28-8: Magnetic force on a current-carrying wire:

If L is a “length vector” of a wire that has a current (i) passing through it, then:

FB = i L x B

Note how the magnetic force is perpendicular to the plane formed by the length vector and the magnetic field and depends on the angle between them!

Checkpoint #5

28-9: Torque on a current loop:

The torque on the circuit due to (uniform) B is:

= x B

Define the magnetic moment of a plane circuit:

= I AHow does it feel to experience a torque?

Do you feel it yet?

Problem 29-40: A single loop, carrying a current of 4.00 A, is in the shape of a right angle triangle with sides 50.0, 120, and 130 cm. The loop is in uniform magnetic field of magnitude 75.0 mT whose direction is parallel to the current in the 130 cm side of the loop.

(a) Find the magnitude of the magnetic force on each of the three sides of the loop.

(b) Show that the total force on the loop is zero!

(c) Find the torque on the current loop.

28-10: The magnetic dipole moment:

U() = - · B

Checkpoint #6

Wfield = - Wappl = -U