Physics 15b Finals Review 01

Electrostatics: Charges and Fields

May 14, 2015

1 Electric Charge

1.1 History

Special relativity grew out of classical electromagnetic theory (Needs no revision)For every kind of particle in nature, as far as we know, there can exist an an-tiparticle, a sort of electrical mirror image that carries the opposite sign.Ex.) (electron, positron), (proton, antiproton), etc.The universe around us consists overwhelmingly of matter, not anti-matter.

1.2 Conservation of Charge

The total electric charge in an isolated system, that is, the algebraic sum of thepositive and negative charge present at any time, never changes.

1.3 Quantization of Charge

The electric charges come in units of charge carried by a single electron (e).Basic units called quarks carry multiples of e

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1.4 Coulombs Law

Two stationary electric charges repel or attract one another with a force propor-tional to the product of the magnitude of the charges and inversely proportionalto the square of the distance between them. :

F2 kq1q2r221

r21 14pi0

q1q2r221

r21

1

SI unit of charge = coulomb (C)

k 14pi0

9 109Nm2{C2

Gaussian system defines k 1. (r cm, F dynes, q esu)Coulombs Law inverse-square dependence + superposition

1.5 Energy of System of Charges

Energy is a useful concept because electrical forces are conservative.The work done in bringing charges q1 and q2 from infinity to r12 is:

W

(applied force) pdisplacementq

r12r8

p 14pi0

q1q2r2qdr 1

4pi0

q1q2r12

The electrical potential energy of a system is a unique property of the final ar-rangement of charges:

U 12

Nj1

kj

1

4pi0

qjqkrjk

where we have defined U 0 to be the state where all the charges are infinitelyfar apart from each other.

1.6 The electric field

The force felt by a charge q0 when brought into a system of charges:

F 14pi0

Nj1

q0qjr20j

r0j

Therefore, we define the electric field:

E 14pi0

Nj1

qjr20j

r0j 14pi0

px1, y1, z1q

r2rdx1dy1dz1

F qE

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1.7 Gausss Law

The electric flux over a surface is defined as:

surface

E da

Gausss Law:

E da 10

i

qi 10

dv

Infinite line charge:

Er 2pi0r

Infinite flat sheet of charge:

Ep 20

1.8 The Force on a Layer of Charge

If the electric field on the left and right of a layer of charges are, E1 and E2,respectively, then by Gausss Law:

E2 E1 0

Inside the layer, since dF Edx A,F

AdF

A x00

Edx E2E1

Ep0dEq 02pE22 E21q

Since E2 E1 0 ,F

A 1

2pE1 ` E2q

1.9 Electric Field Energy

The potential energy U of a system of charges can be calculated directly throughelectric field by simply assigning an energy pE2

2qdv to every volume element dv

and integrating over all space:

U 02

entirefield

E2dv

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Electric ChargeHistoryConservation of ChargeQuantization of ChargeCoulomb's LawEnergy of System of ChargesThe electric fieldGauss's LawThe Force on a Layer of ChargeElectric Field Energy