Magnetic Force

PH 203

Professor Lee Carkner

Lecture 16

Charge Carriers

Imaging a current flowing from top to bottom in a wire, with a magnetic field pointing “in”

If the charge carriers are negative (moving to the top), the magnetic field will also deflect them to the right

The Hall Effect

If it is high the carriers are positive

Since a voltmeter shows the

low potential is on the right, the electron is negative

Hall Quantified

Electrons are now longer deflected and the potential across the strip is constant

but the velocity is the drift speed of the electrons

v = i/neA

n = Bi/eAE Since the potential V = Ed and the thickness of

the strip (lower case “ell”), l = A/dn = Bi/Vle

Electric and Magnetic Force

For a uniform field, electric force vector does not change

Electric fields accelerate particles, magnetic fields deflect particles

Particle Motion

A particle moving freely in a magnetic field will have one of three paths, depending on

Straight line When =

Circle When =

Helix When

This assumes a uniform field that the particle does not escape from

Circular Motion

Circular Motion

This will change the direction of v, and change the direction of F towards more bending

How big is the circle? Magnetic force is F = Centripetal force is F =

We can combine to getr = mv/qB

Radius of orbit of charged particle in a uniform magnetic field

Circle Properties

Circle radius is inversely proportional to q and B

r is directly proportional to v and m

Can use this idea to make mass spectrometer

Send mixed atoms through the B field and they will come out separated by mass

Helical Motion

Charged particles will spiral around magnetic field lines If the field has the right geometry, the particles can become

trapped

Since particles rarely encounter a field at exactly 0 or 90 degrees, such motion is very common

Examples: Gyrosynchrotron radio emission from planets and stars

Helical Motion

Magnetic Field and Current

We know that i = q/t and v = L/t (where L is the length of the wire)

So qv = iL, thus:F = BiL sin

We can use the right hand rule to get the direction of

the force Use the direction of the current instead of v

Force on a Wire

Force on a Loop of Wire

Consider a loop of wire placed so that it is lined up with a magnetic field Two sides will have forces at right angles to

the loop, but in opposite directions The loop will experience a torque

Loop of Current

Torque on Loop

Since = 90 and L = h,F = Bih

The torque is the force times the moment arm (distance to the center), which is w/2

but hw is the area of the loop, A

= iBA

= iBA sin

Torque on Loop

General Loops

= iBAN sin he torque is maximum when the loop is aligned with the field

and zero when the field is at right angles to the loop (field goes straight through loop)

If you reverse the direction of the current at just the right time you can get the coil to spin

Can harness the spin to do work

Next Time

Read 29.1-29.4 Problems: Ch 28, P: 22, 36, 67, Ch 29, P:

1, 27 Test 2 next Friday

A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the right direction?

A) Right

B) Left

C) Up

D) Down

E) Right at you

A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the up direction?

A) Right

B) Left

C) Up

D) Down

E) Right at you

A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce no deflection?

A) Right

B) Left

C) Up

D) Down

E) Right at you