1Electrostatics2210rqqkF =1. Charge force:• Like sign charges repel, unlike sign charges attract.• Coulomb’s Law: direction and magnitude of force between two point charges.2. Force electric field:• Introduced to explain interaction over a distance.• Field lines: start from positive charge, end at negative charge. • More often used as:3. Force charge:• Force moves charge, does work on charge.• Electric potential.4. Electric field charge:• Electric flux:• Electric field originated from charge: Gauss’Law. testqFErr≡EqFrr=∫⋅−=→BArdFUrrB)(A∫⋅≡ SdEErrΦ∫∑=⋅=surfaceenclosedEqSdE0εΦrr2Direct CurrentdtdqI ≡1. Moving charge current:• Electric field inside a conductor keeps the charges moving.• Current direction is defined as the electric field direction.2. Charge electric potential:• Accumulated charge generates potential: capacitance.• Parallel plate capacitor.• Energy stored in a capacitor.3. Current resistance:• Ohm’s law defines resistance.• Resistance as a function of the wire.• Resistance as a linear function of temperature.4. Power• General formula.• With a resistor only (combined with Ohm’s law).VQC ≡dAC0ε=IRV=VIP=RIRVVIP22===[])(1)()(1212TTTRTR−+⋅=αALRρ=CQCVPE222121==3CircuitsneffR...RRR+++=211. Resistors network:• Connection in series, current the same, voltage divided. • Connection in parallel, voltage the same, current divided.• Questions with power: nominal power v.s. actual power.2. Capacitors network:• Connection in series, the same charge, voltage divided.• Connection in parallel, the same voltage, charge divided.3. Kirchhoff’s rules• Loop: • Junction:• Follow the steps.4. RC circuit• Charging.• Discharging.• The time constant.0=∑loopVτteRemfI−=neffR...RRR111121+++=neffC...CCC111121+++=neffC...CCC+++=210=∑junctionIτteRCQI−=RC=τ4Magnetism and Induction1. Current (moving charge) generates magnetic field.• The Biot-Savart law and Ampere’s law.• B-field of a straight wire, at the center of a wire loop, inside a solenoid and the right-hand rules.2. Force on a charge from the E and B fields:• The Lorentz force law.3. Induction of emf from changing magnetic flux.• Motion emf. • Faraday’s law, Lenz law.4. Self-induction and the inductor• Self-induction• Magnetic energy in an inductor• Inductor and the LR circuit.• The LC circuit.LvBemf=dtdILemfself−=RIBπµ20=BvqEqFrrrr×+=dtdsdEemfBΦ−=⋅=∫rr)1(τteRemfI−−=RL=τRIB20µ=InB0µ=221LIPE =τteII−=0LCtIIMAX1)sin(2≡=ωω5Alternating Current and the circuits1. AC• AC voltage power supply.• Average voltage, current and power.2. R, C and L in AC circuit• R, Ohm’s law applies.• C, current leads voltage by 90o• L, voltage leads current by 90o3. RLC in AC circuit• Impedance Z• Phase angle φ• Resonance frequency• Power consumed in an AC circuit.)sin( tVVMAXω=22)(CLXXRZ −+=RXXCL−=ϕtanrmsMAXVV 2=)sin()sin(ϕωϕω+=+= tZVtIIMAXMAXrmsMAXII 2=rmsMAXPP 2=LC,XXCL120==ωϕcos2rmsrmsrmsrmsVIRIp ==6Optics -- reflection1. The law of reflection• Angles in optics are always measured with respect to the normal of the interface.2. Planary mirror• The virtual image has the same distance to the mirror as the object does. • The magnification is 1.3. Spherical mirors• Converging and diverging mirrors.• Focal length and the radius.• Mirror equation and the sign conventions.• The magnification. • The 3-ray diagram.• Multi-mirror problems. irθθ=fddio111=+oioiddhhm −=≡2)(Rf −=7Spherical mirror The 3-ray diagram:Ray 2 starts as an incident ray that passes through the focal point and then reflects parallel to the principal axis. Ray 1 starts as an incident ray that is parallel to the principal axis. It reflects off the mirror and passes through the focal point after it reflects. Ray 3 begins as an incident ray that passes through the center of curvature, strikes the mirror perpendicularly, and reflects back, moving along the same line as the incident ray. hohioioiddhh−=≡Magnification MImage up-side-down, smaller, real8Spherical mirror The 3-ray diagram, convex mirror:Image always upright, smaller, virtual9Optics -- refraction1. Index of refraction• Light travels slower in medium than in vacuum. 2. refraction• Snell’s law • Total internal reflection.3. Lens• Focal length and the radius, lens maker’s equation.• lens equation and the sign conventions.• The magnification. • The 3-ray diagram.• Multi-lens problems. vcn ≡fddio111=+oioiddhhm −=≡2211sinsinθθnn=2121sosin nnnnc>=θ−−=211111RR)n(f−−=211111RR)nn(fmediumlens10Find image with a thin lens Converging lensFFfObjecthodoReal image, inverted, smallerhidioioiddhhm −=≡:ionmagnificat11Find image with a thin lens Diverging lensFFfObjecthodoVirtual image, upright, smallerhidioioiddhhm
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