Electricity and Magnetism

Transcription

1 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 SemiConductors

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

3 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

4 Elementary Particles Atomic Nuclei Weak Force Strength 10 7 Strong Force 100 Atoms Molecules Electric Force 1 Human 1 Earth Solar System Gravity Farthest Galaxy 10 20

5 Coulomb s Law Inverse square law (F ~ 1/r 2 ) Gives magnitude and direction of Force Attractive or repulsive depending on sign of Q 1 Q 2

6 Coulomb s Law F 12 r 21 Q 1 r 21 Q 2

7 Coulomb s Law Q 1 r 21 F 12 = F 21 F 12 r21 Q 2

8 Superposition principle F 13 Q 3 Q 1 F 1,total F 12 Q 2 Note: Total force is given by vector sum Watch out for the charge signs Use symmetry when possible

9 Superposition principle If we have many, many charges Approximate with continous distribution Replace sum with integral!

10 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

11 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

12 Electric Field For a single charge Q Visualize using Field Lines

13 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

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

15 Electrostatic Induction Approach neutral object with charged object Induce charges (dipole) Force between charged and globally neutral object

16 Electric Flux Electric Flux: Φ E = E A Same mathematical form as water flow No substance flowing Flux tells us how much field passes through surface A

17 Electric Flux For complicated surfaces and nonconstant E: Use integral Often, closed surfaces

18 Electric Flux Example of closed surface: Box (no charge inside) da da E Flux in (left) = Flux out (right): Φ E = 0

19 Gauss Law How are flux and charge connected? Charge Q encl as source of flux through closed surface

20 Gauss Law True for ANY closed surface around Q encl Relates charges (cause) and field (effect)

21 Gauss Law Different uses for Gauss Law Field E > Q encl (e.g. conductor) Q encl > Field E (e.g. charged sphere) Proper choice of surface use symmetries

22 Hollow conducting Sphere

23 Gauss Law Charge Sphere radius r 0, charge Q, r > r 0 r 0 Q r da Q encl = Q

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

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

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

27 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

28 Electric Potential Electric Potential Energy proportional to q Define V = U/q Electric Potential V: Units are Volt [V] = [J/C]

29 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

30 Electric Potential for many charges Superposition principle... V(x) = Σ1/(4πε 0 ) Q i /r i Sum of scalars, not vectors! Integral for continous distributions

31 Example: Three charges Q 2 Q 3 Q 1 r 2 r 3 r 1 V(x) = Σ1/(4πε 0 ) Q i /r i x

32 Example: Capacitor plates x=0 a q x a b x b x=d x

33 Example: Capacitor plates x=0 a q x a b x b x=d V(x) 0 U(x,q) x q<0 q>0 x x

34 Applications q Velocity v d Energy for single particle (e.g. electron) small Often measured in Electron Volt [ev] Energy aquired by particle of charge C going through V=1V

35 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