Comments: Yours and Ours

Comments: Yours and Ours

1. Please respect your fellow students - please operate only your own clicker

2. Quite a bit of homework this week and building will be closed Sun/Mon

3. Don’t panic!......Don’t be intimidated by integrals!

Physics 212 Lecture 2, Slide 1

Please go over the integrations one more time and please explain how much mathematical knowledge is expected in this class.Will we need to know how to write an integral like the one shown in the prelecture or in the Question in the prelecture? If so, can we focus a bit more on what each piece means physically?The integrals, they went by too quicklyI found infinite lines of charge to be slightly confusing in terms of the integration

involved. the balloon popping thing was awesome!!! also what the heck is a pre-flight? i know what a pre-lecture is, we had plenty of those in 211, but pre-flight? is that the same as Checkpoint or something? The idea of "force per unit charge" is a little hard to get used to, especially in the idea of which q is which when we write " F/q = K*(q/r^2). Also, what is the r with the pointy accent thing over it at the end of the force equation? It isn't mentioned and doesn't seem to do anything...Electric fields are pretty powerful things. You should go in to more detail about how

awesome they are.

Electricity & Magnetism

Lecture 2

Today’s Concepts:A) The Electric Field

B) Continuous Charge Distributions

Electricity & Magnetism Lecture 2, Slide 2

I find that relating everything to integrals made me very confused. The concept of electric fields

also baffles me - is it simply just a method of quantifying the force from a charge of a specified

amount onto another a specified distance away?

05

If there are more than two charges present, the total force on any given charge is just the vector sum of the forces due to each of the other charges:

+q1 -> -q1 direction reversed

Coulomb’s Law (from last time)

F2,1

F3,1

F4,1

F1

q1

q2

q3

q4

F2,1

F3,1

F4,1

F1

F2,1

F3,1

F4,1

F1

F2,1

F3,1

F4,1

F1

q1

q2

q3

q4

142

14

41132

13

31122

12

21 ˆˆˆ rr

qkqr

r

qkqr

r

qkq++


MATH:

1F

142

14

4132

13

3122

12

2

1

1 ˆˆˆ rr

kqr

r

kqr

r

kq

q

F++

E

09

The electric field E at a point in space is simply the force per unit charge at that point.

Electric field due to a point charged particle

Superposition

E2

E3

E4

E

Field points toward negative andAway from positive charges.

“Can you explain the derivations of the equations for electric fields? ““What is the essence of an electric field? “

Electric Field

q4

q2

q3


q

FE

rr

QkE ˆ

2

i

i

i

i rr

QkE ˆ

2

12

Two equal, but opposite charges are placed on the x axis. The positive charge is placed to the left of the origin and the negative charge is placed to the right, as shown in the figure above.

“I can't figure out the field directions at all.”

CheckPoint


A

Bx

y

+Q -Q

What is direction at point A

a) Up b) down c) Left d) Right e) zero

What is direction at point B

a) Up b) down c) Left d) Right e) zero

15

E

E

CheckPoint

+Q

+Q

+Q

-Q

In which of the two cases shown below is the magnitude of the electric field at the point labeled A the largest? (Select C if you think they are equal)

A

A

Case A Case B

Electricity & Magnetism Lecture 2, Slide 6A B Equal

“Same because

the forces are not

canceling each

other out” “The electric field of

the point charge is

kq/r^2 so if two point

charges are the same

sign the field will be

greater”

“in case B, the two charges

carry same charges, they will

counteract in the line parallel to

the line connecting them”

18

Two charges q1 and q2 are fixed at points (-a,0) and (a,0) as shown. Together they produce an electric field at point (0,d) which is directed along the negative y-axis.

x

y

q1 q2

(-a,0) (a,0)

(0,d)

Which of the following statements is true:

A) Both charges are negativeB) Both charges are positiveC) The charges are oppositeD) There is not enough information to tell how the charges are

related

Two Charges

E


_ _+ +

_+


A B C D

“(A LEFT)In Coulomb's law, the distance is squared, so a doubling of distance is more significant than a doubling of charge. “

“(B RIGHT)The distance is squared, so the charge on the right hand side would need to be 4 times as large for the particle to remain still..”

“(C Still) The +2Q is 2r away from the q so the 2 will cancel out and just be +Q and r which is the same as on the left.”

CheckPoint


INTERESTING: statement is correct, but given in support of “to the left” !!

24


Example

Calculate E at point P.

“Show me more electric field examples, please!”

d

P

d

A) B) C) D)Need to know d

Need to know d & q

E)

What is the direction of the electric field at point P, the unoccupied corner of the square?

0E

( )

-

4cos

24

122

d

q

d

qE

o

x

( )

-

4sin

24

122

d

q

d

qE

o

y

-q +q

+q

i

i

i

i rr

QkE ˆ

2

27

l Q/L

Summation becomes an integral (be careful with vector nature)

“I don't understand the whole dq thing and lambda.”

WHAT DOES THIS MEAN ?

Integrate over all charges (dq)

r is vector from dq to the point at which E is defined

r

dE

Continuous Charge Distributions

Linear Example:

charges

pt for E

dq l dx


i

i

i

i rr

QkE ˆ

2

r

r

dqkE ˆ

2

30

Charge Density

Linear (l Q/L) Coulombs/meter

Surface (s Q/A) Coulombs/meter2

Volume (r Q/V) Coulombs/meter3

What has more net charge?.

A) A sphere w/ radius 2 meters and volume charge density r = 2 C/m3

B) A sphere w/ radius 2 meters and surface charge density s = 2 C/m2

C) Both A) and B) have the same net charge.

“What are the units for charge density (lambda)? .”

Some Geometry

24 RAsphere

3

34 RVsphere LRVcylinder

2

RLAcylinder 2

3

34 RVQA rr

24 RAQB ss

RR

R

Q

Q

B

A

s

r

s

r

3

1

4 2

3

34


10)

CheckPoint


A) (EA<EB) “Electric Field at point A cancels out

to be zero and electric field at point B

experiences E field from both line to move

upward.”

C) (EA>EB) “A gets more of the field because it

is close to both lines of charge. B gets less of

the field because it is close to one and far away

from the other.”

37

“How is the integration of dE

over L worked out, step by step?”

Calculation

2x

dxA) B) C) D) E)

What is ? 2r

dq

22 ha

dx

+22 ha

dx

+

l22)( hxa

dx

+-

l2x

dxl

Charge is uniformly distributed along the x-axis from the origin to x a. The charge density is l C/m. What is the x-component of the electric field at point P: (x,y) (a,h)?

x

y

a

h

P

x

r

dq l dx


We know:

rr

dqkE ˆ

2

40

Calculation

We know:

222 )( hxa

dx

r

dq

+-

l

xx dEE

What is ?

A) B) C) D)

xdE

1cosdE2cosdE

1sindE 2sindE


xa

P

x

r

1 2

2

dq l dx

h

xdE

dE

y


rr

dqkE ˆ

2 We want:

42

We know:

cos2 DEPENDS ON x!

Calculation

2cosdEdEE xx222 )( hxa

dx

r

dq

+-

l

What is ?

A) B)

C) A and B are both OK

xE

+-

a

hxa

dxk

0

222)(

cosl +-

a

hxa

dxk

0

22

2

)(

cosl


xa

P

x

r

1 2

2

dq l dx

h

xdE

dE

y


rr

dqkE ˆ

2

45

We know:

Calculation

2cosdEdEE xx222 )( hxa

dx

r

dq

+-

l


xa

P

x

r

1 2

2

dq l dx

h

xdE

dE

y


rr

dqkE ˆ

2

22 ha

x

+

What is ?

A) B) C) 22 ha

a

+ 22)( hxa

a

+-D)

22 ha

a

+22)( hxa

a

+-22)( hxa

xa

+-

-

2cos

47

We know:

xdE

Calculation

222 )( hxa

dx

r

dq

+-

l 2cosdEdEE xx

222

)(cos

hxa

xa

+-

-

( ) 2/3220 )(

)(hxa

xadxkPE

a

x

+-

- l

What is ? )(PEx

+-

221)(

ah

h

h

kPEx

l

xa

P

x

r

1 2

2

dq l dx

h

xdE

dE

y


rr

dqkE ˆ

2


49

http://www.wolframalpha.com/input/?_=1358440607983&i=integral+from+0+to+a+of+%28a-x%29+%2f+%28%28a-x%29%5e2%2bh%5e2%29%5e%283%2f2%29&fp=1&incTime=true

Homework Problem


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