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January 14, 09 Physics 2102 Physics 2102 Lecture: 03 FRI 16 JAN Lecture: 03 FRI 16 JAN Electric Fields I Electric Fields I Charles-Augustin de Coulomb (1736-1806) Physics 2102 Jonathan Dowling Version: 1/14/09

Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

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Page 1: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

January 14, 09

Physics 2102Physics 2102Lecture: 03 FRI 16 JANLecture: 03 FRI 16 JAN

Electric Fields IElectric Fields ICharles-Augustin

de Coulomb (1736-1806)

Physics 2102

Jonathan Dowling

Version: 1/14/09

Page 2: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

What Are We Going to Learn?What Are We Going to Learn?A Road MapA Road Map

• Electric charge- Electric force on other electric charges- Electric field, and electric potential

• Moving electric charges : current• Electronic circuit components: batteries, resistors,

capacitors• Electric currents - Magnetic field

- Magnetic force on moving charges• Time-varying magnetic field è Electric Field• More circuit components: inductors.• Electromagnetic waves - light waves• Geometrical Optics (light rays).• Physical optics (light waves)

Page 3: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

2q!

12F

1q+

21F

12r

CoulombCoulomb’’s Laws Law

2

12

2112

||||||

r

qqkF =

2

212

00

1085.8with 4

1

mN

Ck

!"== #

$#

2

2

91099.8

C

mN!k =

For Charges in aVacuum

Often, we write k as:

Page 4: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

E-Field is E-Force Divided by E-ChargeE-Field is E-Force Divided by E-Charge

Definition ofElectric Field:

!

! E =

! F

q

!

|! F 12|=

k |q1| |q

2|

r12

2

+q1 –q2

!

! F 12

P1 P2

!

|! E 12|=

k |q2|

r12

2

–q2

!

! E 12

P1 P2

Units: F = [N] = [Newton]; E = [N/C] = [Newton/Coulomb]

E-Forceon

Charge

E-Fieldat

Point

Page 5: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric FieldsElectric Fields

• Electric field E at some point in

space is defined as the force

experienced by an imaginary point

charge of +1 C, divided by 1 C.

• Note that E is a VECTOR.

• Since E is the force per unit charge,

it is measured in units of N/C.

• We measure the electric field using

very small “test charges”, and

dividing the measured force by the

magnitude of the charge.2

||||R

qkE =

–q

R

E+1C

Electric Field of a Point Charge

Page 6: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Superposition of F and ESuperposition of F and E• Question: How do we

figure out the force orfield due to severalpoint charges?

• Answer: consider onecharge at a time,calculate the field (avector!) produced byeach charge, and thenadd all the vectors!(“superposition”)

• Useful to look out forSYMMETRY to simplifycalculations!

Page 7: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Example

• 4 charges are placed at thecorners of a square as shown.

• What is the direction of theelectric field at the center ofthe square?

(a) Field is ZERO!(b) Along +y(c) Along +x

-q

-2q

+2q

+q

y

x

Total electric field

Page 8: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric Field Lines• Field lines: useful way to

visualize electric field E

• Field lines start at apositive charge, end atnegative charge

• E at any point in spaceis tangential to field line

• Field lines are closerwhere E is stronger

Example: a negative pointcharge — note sphericalsymmetry

Page 9: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Direction of Electric Field Lines

E-Field VectorsPoint Away fromPositive Charge —Field Source!

E-Field VectorsPoint TowardsNegative Charge— Field Sink!

Page 10: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric Field of a DipoleElectric Field of a Dipole

• Electric dipole: two pointcharges +q and –qseparated by a distance d

• Common arrangement inNature: molecules,antennae, …

• Note axial or cylindricalsymmetry

• Define “dipole moment”vector p: from –q to +q,with magnitude qd

Cancer, Cisplatin and electric dipoles:http://chemcases.com/cisplat/cisplat01.htm

Page 11: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric Field On Axis of DipoleElectric Field On Axis of Dipole

!+ += EEE :ionSuperposit

2

2!"

#$%

& '

=+

ax

kqE

2

2!"

#$%

&+

'='a

x

kqE

!!!!

"

#

$$$$

%

&

'(

)*+

,+

-

'(

)*+

, -

=22

2

1

2

1

ax

ax

kqE 22

2

4

2

!!"

#$$%

&'

=

ax

xakq

Pa x

-q +qa x

-q +q

Page 12: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric Field Electric Field OnOn Axis of Dipole Axis of Dipole

22

2

22

2

4

2

4

2

!!"

#$$%

&'

=

!!"

#$$%

&'

=

ax

kpx

ax

xakqE

What if x>> a? (i.e. very far away)

p = qa“dipole moment”

a VECTOR

- +

34

22

x

kp

x

kpxE =!

E = p/r3 is actually true for ANY point far from adipole (not just on axis)

3r

pE

!!!

Page 13: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Force on a Charge in Electric FieldForce on a Charge in Electric Field

Definition ofElectric Field:

!

! E =

! F

q

Force onCharge Due toElectric Field:

!

! F = q

! E

Page 14: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Force on a Charge in Electric FieldForce on a Charge in Electric Field

E

E

Positive ChargeForce in SameDirection as E-Field

Negative ChargeForce in OppositeDirection as E-Field

+ + + + + + + + +

+ + + + + + + + +

– – – – – – – – – –

– – – – – – – – – –

Page 15: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin

Electric Dipole in a Uniform FieldElectric Dipole in a Uniform Field• Net force on dipole = 0;

center of mass stays whereit is.

• Net TORQUE τ : INTO page.Dipole rotates to line up indirection of E.

• | τ | = 2(qE)(d/2)(sin θ)= (qd)(E)sinθ= |p| E sinθ= |p x E|

• The dipole tends to “align”itself with the field lines.

• What happens if the field isNOT UNIFORM??

Distance BetweenCharges = d

Page 16: Physics 2102 Jonathan Dowling - LSUphys.lsu.edu/~jdowling/PHYS21022SP09/lectures/03FRI16JAN.pdf · January 14, 09 Physics 2102 Lecture: 03 FRI 16 JAN Electric Fields I Charles-Augustin