Physics 100 Lecture 2

Your Comments

Electricity & Magnetism Lecture 12, Slide 1

I'm having a heck of a time wrapping my head around how this very fundamental stuff can have

an "orientation". Why the heck does a magnetic field cause a force in a direction totally

perpendicular to both the field and the charges movement, and whats to say the force is one

way instead of the other? seems really arbitrary compared to gravity or coulomb's law

Magnetic fields are caused by charges in motion or current, right? How does current flow in

something like a bar magnet? What force drives these charges to move in a bar magnet, why is

it that they can’t just settle out?

Can you play some Led Zeppelin before class again? When the levee breaks was awesome

to listen to before class.

The word lost doesn't do justice to how I'm feeling about the material I just saw. Can I get

some clarification up in this lecture?

I've got a right hand, and I kinda wanna use it....can we go over the right hand rule!!

Dear Professor Stelzor, I am very confused on the direction of a particle in a magnetic field. I

would be so happy and overjoyed if you would be kind enough to explain that to me. If you did I

would be the happiest man EVER! Sincerely, Confused Physics 212 Student

The typo for "north" in question 1 of the prelecture is really bothering me. Also, I meant to do this

prelecture last night after my ECE190 exam, but I was caught up in some E-WEEK shenanigans.

So it's currently 7:30am, and if I don't get a comment post for being clutch, I'll be very

disappointed.

So what is a magnetic field? Please give us the real answer. Kind of like how you can

"conceptually" understand what E=mc^2 actually is.

Physics 212

Lecture 12

Today’s Concept:

Magnetic Force on Moving Charges

BvqF





Electricity & Magnetism Lecture 12, Slide 2

There has been a serious lack of cool demos recently and it is making

me sad. There better be some good demos for this stuff

Today’s Plan:

1) Review of magnetism

2) Review of cross product

3) Example problem

Key Concepts:

1) The force on moving charges due to a magnetic

field.

2) The cross product.

Electricity & Magnetism Lecture 12, Slide 3

Bar Magnets

Compass Needles

N S

S N

N S

N S N S

cut in half

N S

Magnetic Charge?

Magnetic Observations

Electricity & Magnetism Lecture 12, Slide 4

Compass needle deflected by electric current

I

Magnetic fields created by electric currents

Magnetic fields exert forces on electric currents (charges in motion)

I

F

I

F

Magnetic Observations

V

Electricity & Magnetism Lecture 12, Slide 5

RHR

Thumb = current

Fingers = B

Magnetic Observations

Physics 212 Lecture 12, Slide 6

The magnetic field at P points

A. Case I: left, Case II: right B. Case I: left, Case II: left

C. Case I: right, Case II: left D. Case I: right, Case II: right

I (out of the screen)

P

Case I

I (into of the screen)

P

Case II

WHY? Direction of B: right thumb in direction of I,

fingers curl in the direction of B

Magnetism & Moving Charges

All observations are explained by two equations:

Today

BvqF





Next Week

2

0

ˆ

4 r

rsdI

Bd











Electricity & Magnetism Lecture 12, Slide 7

Cross Product Review

Cross Product different from Dot Product

A ● B is a scalar; A x B is a vector

A ● B proportional to the component of B parallel to A

A x B proportional to the component of B perpendicular to A

Definition of A x B

Magnitude: ABsin

q

Direction: perpendicular to plane defined by A and B with sense given by

right-hand-rule

Electricity & Magnetism Lecture 12, Slide 8

x

y

z

B

F

qv

Remembering Directions: The Right Hand Rule

BvqF





Electricity & Magnetism Lecture 12, Slide 9

The particle’s velocity is zero.

There can be no magnetic force.

BvqF





CheckPoint 1a

Electricity & Magnetism Lecture 12, Slide 10

Three points are arranged in a uniform magnetic

field. The B field points into the screen.

A positively charged particle is located at point A and is stationary. The direction of the

magnetic force on the particle is

A. right B. left C. into the screen D. out of the screen

E. zero

CheckPoint 1b

Three points are arranged in a uniform magnetic

field. The B field points into the screen.

X

qv

B

F

BvqF





Electricity & Magnetism Lecture 12, Slide 11

The positive charge moves from A toward B. The direction of the magnetic force on the

particle is

A. right B. left C. into the screen D. out of the screen

E. zero

Cross Product Practice

Protons (positive charge) coming out of screen

Magnetic field pointing down

What is direction of force on POSITIVE charge?

A) Left B) Right C) UP D) Down E) Zero

- x

+ x

+ y

- y

BvqF





x

y

z

B

Electricity & Magnetism Lecture 12, Slide 12

Motion of Charge q in Uniform B Field

x x x x x x x

Uniform B into page

Force is perpendicular to v

Speed does not change

Uniform Circular Motion

Solve for R:

R

Demo

qvBFBvqF 



R

v

a

2



R

v

mqvB

2



q

q q

v

F

v

F

v

F

v

F

q

Electricity & Magnetism Lecture 12, Slide 13

qB

mv

R 

now this is some cool stuff. i hope that there are going to be cool demos in lecture. for the motion

in a uniform field, why doesn't the particle just start accelerating in the positive y direction, instead

of going in a circle? shouldn't the magnetic force always be pointing in the positive direction since

the entire plane is magnetized?

LHC

17 miles diameter

Electricity & Magnetism Lecture 12, Slide 14

qB

p

qB

mv

R 

Can you take us to the LHC (while it is shutdown) to see some of the big magnets in the ring and

the detectors there?

BvqF





CheckPoint 2

The drawing below shows the top view of

two interconnected chambers. Each chamber

has a unique magnetic field. A positively

charged particle is fired into chamber 1, and

observed to follow the dashed path shown in

the figure.

qv

F

B

.

Electricity & Magnetism Lecture 12, Slide 15

What is the direction of the magnetic field in chamber 1?

A. up B. down C. into the page D. out of the page

Observation: R

2

> R

1

The drawing below shows the top view of

two interconnected chambers. Each chamber

has a unique magnetic field. A positively

charged particle is fired into chamber 1, and

observed to follow the dashed path shown in

the figure.

CheckPoint 8

21

BB >

Electricity & Magnetism Lecture 12, Slide 16

qB

mv

R 

Compare the magnitude of the magnetic field in chamber 1 to the magnitude of the

magnetic field in chamber 2

A. |B

1

| > |B

2

| B. |B

1

| = |B

2

| C. |B

1

| < |B

2

|

X X X X X X X X X

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

x

0

x

0

/2

exits here

enters here

d

q,m

Absolutely ! We need to use the definitions of V and E and either conservation of

energy or Newton’s Laws to understand the motion of the particle before it

enters the B field.

We need to use the Lorentz Force Law (and Newton’s Laws) to determine what

happens in the magnetic field.

Conceptual Analysis

What do we need to know to solve this problem?

A) Lorentz Force Law B) E field definition C) V definition

D) Conservation of Energy/Newton’s Laws E) All of the above

)( EqBvqF





+

E

Calculation

Electricity & Magnetism Lecture 12, Slide 17

Strategic Analysis

Calculate v, the velocity of the particle as it enters the magnetic field

Use Lorentz Force equation to determine the path in the field as a function of B

Apply the entrance-exit information to determine B

Let’s Do It !

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

Calculation

Electricity & Magnetism Lecture 12, Slide 18

Physics 212 Lecture 12, Slide 19

Calculation

• Why??

– How do you calculate change in the

electric potential given an electric field?

– What is the relation between the electric

potential amd the potential energy?

• What is the change in the particle’s potential energy after travelling distance d?

(A) (B) (C)

U qEd  -

U Ed  -

0U

V E d Ed  -   -



U q V  

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

Why?

Conservation of Energy

Initial: Energy  U  qV  qEd

Final: Energy  KE  ½ mv

0

2

Newton’s Laws

a  F/m  qE/m

v

0

2

 2ad

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

Calculation

What is v

0

, the speed of the particle as it enters the magnetic field ?

A B C D E

m

E

v

o

2



m

qEd

v

o

2



adv

o

2

md

qE

v

o

2



m

qEd

v

o



qEdmv

o



2

1

m

qEd

v

o

2



m

qEd

v

o

2



d

m

qE

v

o

2



Electricity & Magnetism Lecture 12, Slide 20

Calculation

Why?

Path is circle!

Force is perpendicular to the velocity

Force produces centripetal acceleration

Particle moves with uniform circular motion

X X X X X X X X X

What is the path of the particle as it moves through the magnetic field?

A B C

X X X X X X X X X

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

m

qEd

v

o

2



Electricity & Magnetism Lecture 12, Slide 21

Calculation

Why?

X X X X X X X X X

R

x

o

/2

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

What can we use to calculate the radius of the path of the particle?

A B C D E

o

xR 

o

xR 2

o

xR

2

1



qB

mv

R

o



a

v

R

o

2



m

qEd

v

o

2



Electricity & Magnetism Lecture 12, Slide 22

Calculation

Why?

A B C D E

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

amF





q

mEd

x

B

o

22



q

mEd

x

B

o

21



qEd

m

EB

2



v

E

B 

o

qx

mv

B 

m

qEd

v

o

2



0

2

1

xR 

R

v

mBqv

o

2



R

v

q

m

B

o



m

qEd

xq

m

B

o

22



q

mEd

x

B

o

22



Electricity & Magnetism Lecture 12, Slide 23

Follow-Up

Suppose the charge of the particle is doubled (Q  2q),while keeping the mass

constant. How does the path of the particle change?

A B C

X X X X X X X X X

No slam dunk.. As Expected !

Several things going on here

1. q changes -> v changes

2. q & v change -> F changes

3. v & F change -> R changes

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

q

mEd

x

B

o

22



Electricity & Magnetism Lecture 12, Slide 24

Follow-Up

How does v, the new velocity at the entrance, compare

to the original velocity v

0

?

Why?

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

q

mEd

x

B

o

22



2

1

2

1

22

o

mvqEdQEdmv 

A B C D E

2

o

v

v 

o

vv 

o

vv 2

o

vv 2

2

o

v

v 

22

2

o

vv 

o

vv 2

Suppose the charge of the particle is doubled (Q  2q),while keeping the mass

constant. How does the path of the particle change?

Electricity & Magnetism Lecture 12, Slide 25

Follow-Up

How does F, the magnitude of the new force at the entrance, compare

to F

0

, the magnitude of the original force?

Why?

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

Suppose the charge of the particle is doubled (Q  2q),while keeping the mass

constant. How does the path of the particle change?

q

mEd

x

B

o

22



o

vv 2

BvqQvBF

o

 22

A B C D E

2

o

F

F 

o

FF 

o

FF 2

o

FF 2

o

FF 22

o

FF 22

Electricity & Magnetism Lecture 12, Slide 26

Follow-Up

How does R, the radius of curvature of the path, compare to R

0

, the

radius of curvature of the original path?

Why?

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

Suppose the charge of the particle is doubled (Q  2q),while keeping the mass

constant. How does the path of the particle change?

A B C D E

2

o

R

R 

2

o

R

R 

o

RR 

o

RR 2

o

RR 2

R

v

mF

2



o

vv 2

o

FF 22

F

v

mR

2



Electricity & Magnetism Lecture 12, Slide 27

2222

2

22

o

R

F

v

m

F

v

mR 

q

mEd

x

B

o

22



Follow-Up

A particle of charge q and mass m is accelerated from

rest by an electric field E through a distance d and

enters and exits a region containing a constant magnetic

field B at the points shown. Assume q,m,E,d, and x

0

are

known.

What is B?

B

X X X X X X X X X

B

x

0

x

0

/2

exits here

enters here

d

q,m

E

B

A B C

X X X X X X X X X

Suppose the charge of the particle is doubled (Q  2q),while keeping the mass

constant. How does the path of the particle change?

2

o

R

R 

A Check: (Exercise for Student)

Given our result for B (above), can you show:

Q

mEd

B

R

21



2

o

R

R 

Electricity & Magnetism Lecture 12, Slide 28

q

mEd

x

B

o

22

