University Physics Final Exam Overview

21. Electric Field How is electric field defined? How to find the electric field arising from a point charge? How to find the force on a charge if the electric field at the point is known?

Typical Problems + Using superposition principle to find the resultant of electric fields. - The path of a charge being bent in an electric field. Make analogy to projectile motion.

22. Gauss’s Law Gauss’s law is the integral form of Coulomb’s law. It provides a versatile path to the finding of electric fields arising from distribution of charges. We only use Gauss’s law on problems of high symmetry.

Applications of Gauss’s Law http://www.cartage.org.lb/en/themes/sciences/physics/Electromagnetism/Electrostatics/Gaussslaw/Gaussslaw/Applications/gappc.gif

Typical Problems Electric field inside or outside of a non-conducting sphere Electric field inside or outside of concentric conducting spheres +1 +2 +4 - + a b c d

23. Electric Potential How is electric potential defined? U = qV Electric potential V is the energy property (or scalar property) of the space around a source charge, whereas electric field E is the force property (or vector property) of the space around a source charge.

Relations Between E and V E -> V V -> E

E and V Conversions For a point charge For a parallel plate capacitor

Typical Problems Find the speed of a charge at far distance when released from a stationary charge. Find the potential energy stored in a configuration of charges. Qi + a a + a + Qii Qiii

24. Capacitors What is a capacitor? How is capacitance defined in a circuit? C=Q/V How is capacitance determined by the geometry of a capacitor? What is the energy stored in a capacitor?

The Equivalent Capacitance Capacitors linked in series Capacitors linked in parallel

Typical Problems Circuit analysis with composite capacitors A B II I 1.0 A B 2.0 3.0 4.0 5.0 12 18 II I III IV

25. Current and Resistance Current is the rate of transfer of charge. Resistance can be measured from Ohm’s law. Resistance is determined by the material and the geometry.

Electrical Power The electric power consumed on a resistor.

26. DC Circuits Equivalent resistance for connection in series Equivalent resistance for connection in parallel

Kirchhoff’s Point Rule and Loop Rule Point rule or Kirchhoff’s current rule Loop rule or Kirchhoff’s voltage rule iR2 e1 I e2

Mesh Analysis Typical problems 5.0 W i2 = 7/3 – i3 i3 + _ e 5.0 W 15 V

27. Magneticl Field How does magnetic field exert force on a moving charge? How does magnetic field exert force on a current? How does magnetic field exert torque on a current carrying loop? with

The Potential Energy in a Current Loop The magnetic potential energy stored in a current-carrying loop is= with

Circular Motion of a Charge in a B Field The magnetic force provides the exact amount of centripetal force

28. Ampere’s Law I B How is magnetic field generated from a loop of current? How is magnetic field generated from a long wire of current?

The Interaction between two current carrying wires BI1 BI2 x x Fwire1- BI2 Fwire2-BI1 Wire 1 Wire 2

Magnetic Field in a Solenoid How to use Ampere’s law to find the B field inside a solenoid Ampere’s Law

29. Faraday’s Law How is emf induced from a change of magnetic flux? How is emf induced in a conducting rod moving across a B field

Lenz’s Law The key word “opposing” can find two applications: How to determine the direction of the induced current? The key word “opposing” can find two applications: If Foriginal increases, Binduced directs opposite to Borigial; If Foriginal decreases, Binduced directs in the same direction as Borigial;

30. Inductance How does inductance relate the rate of change of current to the induced emf? For one coil: For two coils:

Inductance and Magnetic Flux For self-inductor For mutual-inductor

Energy Stored in a Self-Inductor

31. Alternating Currents How is the resistive effect quantified for R, L, C in an AC circuit? Resistance Inductive reactance Capacitive reactance

Impedance The effective resistance of the entire circuit is called impedance Z An analog of Ohm’s law holds in the entire circuit as

Phasor Diagram VL and VC are on the same line and so the net y component is VL – VC The phase angle q can be determined from the phasor diagram as

Power Expenditure in AC Circuit The power in an AC circuit is consumed only by the resistor. The consumption rate is P = IrmsVR = IrmsVrms cosq cosq is called the power factor of the circuit

The Resonance Condition for RLC Circuit The maximum flow of current occur in an RLC circuit when