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ELECTRIC FIELDS

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A CLOSER LOOK AT CHARGES AND FORCES

Recall Coulombs Law:2

212112

rqqkFF

F12= force exerted by q2on q1 when q1 is placed at a distance

r from q2F21= force exerted by q1 on q2when q2is placed at a distance

r from q1 action at a distance

How does either charge knows that the other charge is placedat a distance r from it?

Ans: One charge sets up an electric fieldaround it.

The second charge placed nearby interacts with the field and

experiences a force due to the field of the first one.

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(Fig b) A charged object sets up an electric field Eat point P

(and everywhere else around it of course).

(Fig a) A charge (positive) q0placed at P interacts with the field

and experiences a force Fin the direction of the field E

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THE ELECTRIC FIELD

defined)field(electric0q

FE

Electric Field : force per unit charge that a charge qo

experiences in a region of space where the electric field is setup by a source charge.

Unit: Newtons per Coulomb; N/C

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Electric Field Lines

used to visualize electric fields

the direction of a straight line or of the tangent to a curved linegives the direction of the field at a given point

the density of the lines is proportional to the magnitude of the

field

applet1

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Electric field lines (a) extend away from positive

charge and (b) toward negative charge.

applet1

http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.htmlhttp://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html

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(a) a positive test charge near a portion

of an infinitely large non-conducting

sheet(or plane) with uniform charge

distribution on one side

(b) Efield vector at location of testcharge;

field lines in space near the

sheet.

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Electric dipole

pair of charges of equal magnitude but opposite sign

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A pair of like charges with

field lines around them

2d Field

3d Field

http://www.falstad.com/vector2de/http://www.falstad.com/vector3de/http://www.falstad.com/vector3de/http://www.falstad.com/vector2de/

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Electric Field Due To A Point Charge

2

0

r

qqkF

Force between q and q0 Force on q0due to q

2

0 r

qk

q

FE electric field due to point charge q

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Net force on q0due to charges q1, q2, q3, qn :

F0= F01+ F02+ F03+ .+ F0n

n

n

qqqqq

EEEE

FFFFFE

.......

........

q.......,,q,q,qtodueqofpositionatfieldNet

321

0

0

0

03

0

02

0

01

0

0

n3210

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Electric Field Due To A Dipole

Field at point P(a distance z from dipole midpoint):

2

0

2

0 41

41

rq

rq

EEE

2

2

2

2

21

2

1

z

dzdzr

2

2

2

2

21

2

1

z

dzdzr

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Hence we get:

1/ 22 2

20

20

20

1 1

2 24

2 21 1 (using binomial expansion)

2 1! 2 1!4

1 14

q d dE

z zz

q d d

z zz

q d d

z zz

3

0

2

02

12

4 z

qd

z

d

z

qE

magnitudemomentdipoleelectricqdp

E

dipole)(electric2

13

0 z

pE

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Electric Field Due to A Line Charge

= line charge distribution= Q/L = dq/ds

dq = ds

2220

2

0

2

0

41

4

1

4

1

Rzds

r

ds

r

dqdE

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2122cos

Rz

z

r

z

ds

Rz

zdE

2322

04cos

23220

2

0

2322

0

4

2

4

cos

Rz

Rz

ds

Rz

z

dEE

R

Rq 2

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Find the electric field at point P due to the bent rod with

charge Q uniformly distributed along the bent rod.

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2

0

2

0 41

41

rds

rdqdE

)(rcos4

1cos

4

1cos

2

0

2

0

d

rds

rdEdEx

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r

r

rd

r

dr

dEE x

0

00

0

60

60

0

60

600

60

60

2

0

4

73.1

6060sin4

sin4

cos4

1

cos4

1

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R

drrrzz

dEE0

2/322

0

24

1

.2and,,Setting1

2322

mX

dXX

drrdXmrzXm

m

R

rzzE

021

2/1

22

04

disk)(charged12 220

Rz

z

E

sheet)(infinite2

,RAs0

E

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A Point Charge In An Electric Field

EF q E= electric field

q = point charge

F = electrostatic force; same direction as Efor (+)q;

opposite direction of Efor (-)q

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Dipole In An Electric Field

sinsin2

sin2

:dipoleonnet torqueofMagnitude

Fdd

Fd

F

UsingF=qEandp=qd :

sinpE

dipole)on(torqueEp

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Potential Energy of an Electric Dipole

in the diagram E tends to rotate pclockwise towards = 0

= -pEsinfor clockwise rotation

potential energy is work W done

against Ein rotating pfrom to 900

potential energy is work (-)W doneby Ein the opposite sense, from 900

to .

9090

90

90

sinsin dpEdpE

ddWU

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cos

g,Integratin

pEU

dipole)ofenergy(potentialEp

U