Experimental Physics IIa - Electric charge, field, dipole 1

Experimental Physics EP2a

Thermodynamics & Electricity

– Electric charge –Conductors, Coulomb’s law

https://bloch.physgeo.uni-leipzig.de/amr/

Experimental Physics IIa - Electric charge, field, dipole 2

Electric chargeAir

Human Hands

Asbestos

Glass

Human Hair

Mica

Nylon

Wool

Lead

Silk

Aluminum

Paper

Cotton

Steel

Wood

Rubber balloon

Hard rubber

Nickel, Copper

Brass, Silver

Gold, Platinum

Sulfur

Celluloid

Silicon

Teflon

+

-

Benjamin FranklinJanuary 17, 1706 Boston

April 17, 1790 Philadelphia

+ -

-

+ +

-

e = 1.602177 ´ 10-19 C

-e

+e

Charge is conserved.

Experimental Physics IIa - Electric charge, field, dipole 3

Conductors and insulators

+ + + + + +

+++++

++++

+

++

--

-

---

---

---

++

++

+

++

+++

++

--- -

--

-

--

-

- -

+ + + + + + --

---

--

--

-

-

-+

++

+

+

+

+ +

++++-

-- -

-

-

-

--

-

- -

++

++

+

++

+++

++

Experimental Physics IIa - Electric charge, field, dipole 4

Coulomb’s law

The force exerted between two charges acts along the line connecting the charges.

It varies inversely proportional to the square of the distance separating the charges.

It is proportional to the product of the charges.

The force is repulsive if the charges have the same sign and attractive if they are opposite.

2,122,1

212,1 r̂

rqkqF =

!22,1

212,1 r

qqkF =

1 22,1r!

229 /CmN109875.8 ×´=k

( ) 104 -= pek

Experimental Physics IIa - Electric charge, field, dipole 5

Some examples

e = 1.6 ´ 10-19 Cmp = 1.67 ´ 10-27 kgme = 9.11 ´ 10-31 kgG = 6.67 ´ 10-11 N m2 kg-2

?-g

e

FF

nC11 =q nC21 -=q

nC11 =qm103.5 11-´=r

?-eF ?-a

Experimental Physics IIa - Electric charge, field, dipole 6

To remember!

Ø Unlike charges attract one another, like charges repel.

Ø Charge is conserved.

Ø Charge is quantized – integer number of electronic charge.

Ø Conductors are materials in which electrons move freely.

Ø In insulator electrons do not move freely.

Ø Coulomb’s law states that force due to charges:

(i) inversely proportional to square distance,

(ii) proportional to the product of charges,

(iii) the proportionality constant is calledthe Coulomb constant.

Electric field

-321 FFFF ++=+

-

q0+3F

F!

2F

1F

Experimental Physics IIa - Electric charge, field, dipole 7

00/lim

0

qFEq ®

=

•q0 is a test charge(i.e. q0 is small enoughto not alter the electric field)• q0 is positive

131/1 -- ×××= AsmkgCN mV /1=

Electric field

PiPi

iPi rrkqE ,2,

, ˆ=

Coulombs law:

åå ==i

PiPi

i

iPiP r

rkqEE ,2,

, ˆ

-

PiE ,

iq

Pir ,!

P

net electric field, due to a distribution of point charges

electric field, due to charge qi at point P

Experimental Physics IIa - Electric charge, field, dipole 8

Electric field lines

Øelectric field lines (also lines of force) show thedirection of the force exerted on a positive testcharge

Øthe electric field lines point radially away frompositive charges and towards negative charges

Øthe density (spacing) of the lines isproportional to the electric field strenght at that point

Øfield lines do not cross

Øthe number of lines leaving or entering a charge is proportional to the magnitude of thecharge

Øelectric field lines begin on positive charges (orinfinity) and end on negative charges (orinfinity)

+

Experimental Physics IIa - Electric charge, field, dipole 9

monopole2 opposite charges2 equal chargesequal charges, but different magnitude)opposite charges with different magnitudes

Electric field lines

Experimental Physics IIa - Electric charge, field, dipole 10

Motion of a Point Charge in the Electric Field

Emq

mF

a ==å!

example: electron in uniform electric field

CkNEx /1=

- 0v!

e

smv x /102 6,0 ×=

meE

mF

a xx

-==

E

x

xx

avv

x2

2,0

2 -=D cm

eEmv

x x 14.12

2,0 ==D0=xv

How far can it travel until it is momentarily stopped?

the rest is mechanics…

Experimental Physics IIa - Electric charge, field, dipole 11

Motion of point-like charges in electric fields

compare with physics of throws (mechanics, EP1)

Experimental Physics IIa - Electric charge, field, dipole 12

Electric dipoles

+-L

p!

Lqp = q+q-

A system of two equal and opposite charges q separated by a small distance L ia called an electric dipole

the electric dipole moment:

points from the negative to thepositive charge and has the lengthp || Lq

++

-p

Experimental Physics IIa - Electric charge, field, dipole 13

Electric dipoles

)cosˆ3()( 3 prprkrE !""

-×= Jthe field of an electric dipol

Experimental Physics IIa - Electric charge, field, dipole 14

Electric dipoles in external electric fields

+

-p!

Q

q+

q-2F!

1F!E

!

Ep!!!

´=ttorque on the dipole

QQ=Q= dpEddW sintwork done by electric field, when the dipol rotates:

potential energy:

EppEU!!

-=Q-= cos

uniform electric field:

Experimental Physics IIa - Electric charge, field, dipole 15

Electric Dipoles in External Electric Fields nonuniform electric field:

+

-p!

q+

q-

+

1F!

2F!

12 FF!!

>

a net force actson the dipole

example: a dipole in the fieldof a positive point charge

Experimental Physics IIa - Electric charge, field, dipole 16

To remember!

Ø Charges produce electric fields .

Ø Electric field exerts force on (other) charges.

Ø Electric field is defined by measuring the force on a test charge with an infinitely small charge.

Ø Electric field lines are used to visualize the electric field

Ø Dipoles have no net charge.

Ø Dipoles have an electric dipole moment p.

Ø Electric field of a dipole is proportional p/r3.

Ø In electric fields a torque may act on dipoles .

Experimental Physics IIa - Electric charge, field, dipole 17