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Electrostatics 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: q1q2 F k0 2 r F E qtest F qE 3. Force charge: • • Force moves charge, does work on charge. Electric potential. 4. Electric field charge: • • A Electric flux: Electric field originated from charge: Gauss’ Law. E U (A B) F dr B enclosed surface E E dS q E dS 0 1 Direct Current 1. Moving charge current: • • Electric field inside a conductor keeps the charges moving. Current direction is defined as the electric field direction. I dq dt 2. Charge electric potential: • • • Accumulated charge generates potential: C Q C A 0 capacitance. V d Parallel plate capacitor. 1 1 Q2 2 Energy stored in a capacitor. PE CV 2 3. Current resistance: • • • Ohm’s law defines resistance. Resistance as a function of the wire. Resistance as a linear function of temperature. 4. Power • • 2 C L V IR R A R(T2 ) R(T1 ) 1 (T2 T1 ) General formula. With a resistor only (combined with Ohm’s law). P VI V2 P VI I 2R R 2 Circuits 1. 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. V loop I 0 t emf I e R Reff R1 R2 ... Rn 1 1 1 1 ... Reff R1 R2 Rn 1 1 1 1 ... Ceff C1 C2 Cn Ceff C1 C2 ... Cn junction 0 t Q I e RC RC 3 Magnetism and Induction 1. 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 righthand rules. 2. Force on a charge from the E and B fields: • The Lorentz force law. 0 I 0 I B B B 0 In 2R 2R F qE qv B 3. Induction of emf from changing magnetic flux. • • d B emf LvB emf E ds dt 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. I I MAX sin( t ) 2 1 LC emf self dI L dt 1 2 PE LI 2 t emf I (1 e ) R I I 0e t L R 4 Alternating Current and the circuits 1. AC • • AC voltage power supply. Average voltage, current and power. VMAX 2Vrms V VMAX sin( t ) PMAX 2 Prms I MAX 2I rms 2. R, C and L in AC circuit • • • R, Ohm’s law applies. C, current leads voltage by 90o L, voltage leads current by 90o 3. RLC in AC circuit • • Impedance Z Phase angle φ I I MAX sin( t ) VMAX sin( t ) Z Z R 2 ( X L X C )2 tan • Resonance frequency 1 X L XC , LC • Power consumed in an AC circuit. 2 prms I rms R I rmsVrmscos X L XC R 2 0 5 Optics -- reflection 1. The law of reflection • r i 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 • • • • • • R f ( ) 2 Converging and diverging mirrors. Focal length and the radius. Mirror equation and the sign conventions. h d The magnification. m i i ho do The 3-ray diagram. Multi-mirror problems. 1 1 1 do di f 6 Spherical mirror The 3-ray diagram: Magnification M 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. hi d i ho do h o hi 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. Image up-side-down, smaller, real 7 Spherical mirror The 3-ray diagram, convex mirror: Image always upright, smaller, virtual 8 Optics -- refraction 1. Index of refraction • Light travels slower in medium than in vacuum. 2. refraction • • Snell’s law Total internal reflection. n n1sin 1 n2sin 2 n1sin c n2 so n1 n2 3. Lens • • • • • c v Focal length and the radius, lens maker’s equation. lens equation and the sign conventions. The magnification. The 3-ray diagram. Multi-lens problems. 1 1 1 ( n 1 ) f R1 R2 1 1 nlens 1 ( 1 ) f nmedium R1 R2 1 1 1 do di f m hi d i ho do 9 Find image with a thin lens Converging lens h o F d o Object F hi di magnificat ion : m ho do f di hi Real image, inverted, smaller 10 Find image with a thin lens Diverging lens h o d o Object hi F F di Virtual image, upright, smaller f hi di magnificat ion : m ho do 11