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Summary of the First Chapter of Purcell's E&M
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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
3
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
2
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
3
Electric ChargeHistoryConservation of ChargeQuantization of ChargeCoulomb's LawEnergy of System of ChargesThe electric fieldGauss's LawThe Force on a Layer of ChargeElectric Field Energy
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