Magnetic Force

Physics 102Professor Lee

CarknerLecture 18

PAL #17 Magnetic Field

Direction electron is fired into magnetic field that points north if it is deflected up

Force equation: F = qvB sin = sin-1 [(1.7X10-14)/((1.6X10-19)(3X105)

(0.5))] = v vector points 45 west of north, which is

pointed northwest, so electron was fired from southeast

Electron in B Field

vB

North

West

South

East

From right hand rule:

B is north and force is up so v is from west

(reversed to east for electron)

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) RightB) LeftC) UpD) DownE) 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) RightB) LeftC) UpD) DownE) 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) RightB) LeftC) UpD) DownE) Right at you

Electric and Magnetic Force How do the electric and magnetic forces differ?

Dependences Magnetic force depends on v and , as well as B and q

Vector

Force vector does change for a magnetic field, since as the particle is deflected the v vector changes

Particle Motion A particle moving freely in a magnetic field will

have one of three paths, depending on Straight line

Circle

Helix

This assumes a uniform field that the particle

does not escape from

Circular Motion

Circular Motion If the particle moves at right angles to the field the

force vector will cause the path to bend

The particle will move in a circle 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 they will

come out separated by mass

Today’s PAL

How long would it take an electron to complete one circular orbit around a 1 G magnetic field?

Helical Motion If the initial velocity is not completely perpendicular

to the field, instead of a circle you get a spiral or helix Charged particles will spiral around magnetic field

lines

For example, if the lines begin and end at a pole

Examples: Gyrosynchrotron radio emission from planets and stars

Helical Motion

Solar Wind Particles in Earth’s Magnetic Field

Magnetic Field and Current Since a current is moving charge, a magnet

will produce a force on a wire with a current flowing through it

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 For a loop of width w and height h, force is F = BIL sin

for each long side Since = 90 and L = h,

The torque is the force times the moment arm

(distance to the center), which is w/2 Total torque = but hw is the area of the loop, A

If the field is at angle to the loop then

Torque on Loop

General Loops If there are multiple loops (N), the torque is the sum of

each = IBAN sin

A loop placed along a magnetic field will try to align such that the field goes straight through it

Can harness the spin to do work Called a motor

Next Time

Read 20.7-20.8 Homework: Ch 20, P 4, 17, 38, 49 Exam #2 Friday