Electricity and Magnetism

• Review – Electric Charge and Coulomb’s Force – Electric Field and Field Lines – Superposition principle – E.S. Induction – Electric Dipole – Electric Flux and Gauss’ Law – Electric Potential Energy and Electric Potential – Conductors, Isolators and Semi-Conductors

Feb 27 2002 Today

• Fast summary of all material so far – show logical sequence – help discover topics to refresh for Friday

Feb 27 2002 Electric Charge and Electrostatic Force

• New Property of Matter: Electric Charge –comes in two kinds: ‘+’and ‘-’ •Connected toElectrostatic Force –attractive(for ‘+-’) or repulsive (‘--’, `++’) •Charge is conserved •Charge isquantized

Feb 27 2002 Strength 10-20 -7 Elementary Particles Weak Force 10 Atomic Nuclei 10-15 Strong Force 100

Atoms 10-10 Molecules Electric Force 1 10-5

Human 1

Earth 105 -36 1010 Gravity 10 Solar System 1015 1020 Feb 27 2002 Farthest Galaxy Coulomb’s Law

• Inverse square law (F ~ 1/r2) • Gives magnitude and direction of Force • Attractive or repulsive depending on

sign of Q1Q2

Feb 27 2002 Coulomb’s Law

F12

r21 Q1

Q r21 2

Feb 27 2002 Coulomb’s Law

r21 Q1 F12 = - F 21 F12 r 21 Q2

Feb 27 2002 Superposition principle

Q3

F13

Q1 F1,total F12 Q2 •Note: – Total force is given by vector sum – Watch out for the charge signs – Use symmetry when possible

Feb 27 2002 Superposition principle

• If we have many, many charges – Approximate with continous distribution • Replace sum with integral!

Feb 27 2002 Electric Field

• New concept – Electric Field E • Charge Q gives rise to a Vector Field

•E is defined by strength and direction of force on small test charge q

Feb 27 2002 The Electric Field

• Electric Field also exists is test charge q is not present • The charge Q gives rise to a property of space itself – the Electric Field • For more than one charge -> Superposition principle

Feb 27 2002 Electric Field

• For a single charge

+Q

• Visualize using Field Lines

Feb 27 2002 Field Lines

• Rules for field lines – Direction: In direction of E at each point – Density: Shows magnitude of E – Field Lines never cross – From positive to negative charge • i.e. show direction of force on a positive charge – Far away: Everything looks like point charge

Feb 27 2002 Electric Dipole

Torque τ = p x E p = Q l Dipole moment

Feb 27 2002 Electrostatic Induction

• Approach neutral object with charged object + ++ --++ • Induce charges (dipole) + + - + + + - ++ • Force between charged and + + - + + + globally neutral object

Feb 27 2002 Electric Flux

• Electric Flux: ΦE = E A • Same mathematical form as water flow •No ‘substance’flowing • Flux tells us how much field ‘passes’ through surface A

Feb 27 2002 Electric Flux

• For ‘complicated’ surfaces and non-constant E: –Use integral

• Often, ‘closed’ surfaces

Feb 27 2002 Electric Flux

• Example of closed surface: Box (no charge inside)

dA dA

E

• Flux in (left) = -Flux out (right): ΦE = 0

Feb 27 2002 Gauss’ Law

• How are flux and charge connected?

•Charge Qencl as source of flux through closed surface

Feb 27 2002 Gauss’ Law

• True for ANY closed surface around Qencl • Relates charges (cause) and field (effect)

Feb 27 2002 Gauss’ Law • Different uses for Gauss’ Law

– Field E -> Qencl (e.g. conductor)

– Qencl -> Field E (e.g. charged sphere) • Proper choice of surface – use symmetries

Feb 27 2002 Hollow conducting Sphere

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Feb 27 2002 Gauss’ Law

• Charge Sphere radius r0, charge Q, r > r0

dA Q r0

r

Qencl = Q

Feb 27 2002 Gauss’ Law

• Most uses of Gauss’ Law rely on simple symmetries – Spherical symmetry – Cylinder symmetry –(infinite) plane • and remember, E = 0 in conductors

Feb 27 2002 Work and Potential Energy F(l) b dl x α x Work: a Conservative Force:

Potential Energy

Feb 27 2002 Electric Potential Energy

• Electric Force is conservative – all radial forces are conservative (e.g. Gravity) • We can define Electric Potential Energy

F

Feb 27 2002 Example: Two charges

Q q

r

•If q,Q same sign: – U > 0; we have to do work ‘pushing’ charges together •If q,Q unlike sign: – U < 0; Electric force does work ‘pulling’ charges together Feb 27 2002 Electric Potential

• Electric Potential Energy proportional to q •Define V = U/q

• Electric Potential V: – Units are Volt [V] = [J/C]

Feb 27 2002 Electric Potential

• Note: because V = U/q -> U = V q – for a given V: U can be positive or negative, depending on sign of q • V :Work per unit charge to bring q from a to b

•Ex.:Single Charge

Feb 27 2002 Electric Potential for many charges

• Superposition principle....

V(x) = Σ1/(4πε0) Qi/ri

• Sum of scalars, not vectors! • Integral for continous distributions

Feb 27 2002 Example: Three charges

Q2

Q3

Q1 r2 r3

r1 V(x) = Σ1/(4πε0) Qi/ri

x

Feb 27 2002 Example: Capacitor plates

+ - + - + - + - + - + a b - + +q - + - + - + - x x a b x x=0Feb 27 2002 x=d Example: Capacitor plates V(x) 0 + - x + - + - + - + - a b + - U(x,q) q<0 + +q - + - + - x + - x x a b x x=0Feb 27 2002 x=d q>0 Applications

+ - + - + - • Energy for single particle + (e.g. electron) small Velocity v - + - +q •Often measured in + - ‘Electron Volt’[eV] + - + - • Energy aquired by + - particle of charge 10-19 C + - going through ∆V=1V d Feb 27 2002 Conductors

•E = 0 inside – otherwise charges would move • No charges inside –Gauss • E perpendicular to surface – otherwise charges on surface would move • Potential is constant on conductor

Feb 27 2002