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## Exam 2 covers Ch. 27-33, Lecture, Discussion, HW, Lab

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**Exam 2 covers Ch. 27-33,Lecture, Discussion, HW, Lab**Exam 2 is Tue. Oct. 27, 5:30-7 pm, 145 Birge • Chapter 27: The Electric Field • Chapter 29: Electric potential & work • Chapter 30: Electric potential & field • (exclude 30.7) • Chapter 31: Current & Resistance • Chapter 32: Fundamentals of Circuits • (exclude 32.8) • Chapter 33: The Magnetic Field • (exclude 33.5-33.6, 33.9-10, & Hall effect)**Electric field lines**• Local electric field tangent to field line • Density of lines proportional to electric field strength • Fields lines can only start on + charge • Can only end on - charge. • Electric field lines can never cross Physics 208 Lecture 15**4**3 1 2 Question Here is a picture of electric field lines. Which choice most accurately ranks the magnitude of the electric field at the different points? E1=E3>E2=E4 E1=E2>E3>E4 E4=E3>E1=E2 E4=E2>E1>E3 E4<E3<E1<E2 Physics 208 Lecture 15**Charge Densities**• Volume charge density: when a charge is distributed evenly throughout a volume • = Q / V dq = dV • Surface charge density: when a charge is distributed evenly over a surface area • = Q / A dq = dA • Linear charge density: when a charge is distributed along a line • = Q / dq = d Electric fields and potentials from these charge elements superimpose Physics 208 Lecture 15**Infinite line of charge, charge density λ**r + + + + + + + + + + + + + + + + + + + + r Infinite sheet of charge, charge density η Physics 208 Lecture 15**Ring of uniform positive charge**A) B) C) D) E) Which is the graph of on the z-axis? z y x z Physics 208 Lecture 15**Properties of conductors**- - + + - + - + - - + + • everywhere inside a conductor • Charge in conductor is only on the surface • surface of conductor**Electric potential: general**Electric potential energy difference U • Electric field usually created by some charge distribution. • V(r) is electric potential of that charge distribution • V has units of Joules / Coulomb = Volts Electric potential difference Depends only on charges that create E-fields**Electric Potential**Electric potential energy per unit chargeunits of Joules/Coulomb = Volts Example: charge q interacting with charge Q Electric potential energy Electric potential of charge Q Q source of the electric potential, q ‘experiences’ it**Example: Electric Potential**y Calculate the electric potential at B B x d d2=4 m -12 μC +12 μC A - + Calculate the electric potential at A d1=3 m 3 m 3 m Calculate the work YOU must do to move a Q=+5 mC charge from A to B. Work done by electric fields**Potential from electric field**• Electric field can be used to find changes in potential • Potential changes largest in direction of E-field. • Smallest (zero) perpendicular to E-field V=Vo**Electric Potential and Field**y A 5m B 2m x 2m 5m Uniform electric field of What is the electric potential difference VA-VB? A) -12V B) +12V C) -24V D) +24V**Capacitors**Conductor: electric potential proportional to charge: C = capacitance: depends on geometry of conductor(s) Example: parallel plate capacitor +Q -Q Area A d Energy stored in a capacitor:**Question**What is the voltage across capacitor 1 after the two are connected? C1=1µF C2=3µF V1=1V V2=0V 1V 2V 0V 0.25V 4V**Isolated charged capacitor**• Plate separation increased • The stored energy • Increases • Decreases • Does not change Stored energy A) B) C) q unchanged because C isolated q is the same E is the same = q/(Aε0) ΔV increases = Ed C decreases U increases**Conductors, charges, electric fields**• Electrostatic equilibrium • No charges moving • No electric fields inside conductor. • Electric potential is constant everywhere • Charges on surface of conductors. • Not equilibrium • Charges moving (electric current) • Electric fields inside conductors -> forces on charges. • Electric potential decreases around ‘circuit’**Resistance and resistivity**• Ohm’s Law: ΔV = R I (J = σE or E = ρJ) • ΔV = EL and E = ρ J => ρ I/A = ΔV/L • R = ρL/A Resistance in ohms (Ω) I Question A block is made from a material with resistivity of 10-4Ω-m. It has 10 A of current flowing through it. What is the voltage across the block? 0.1V 0.25V 0.5V 1.0V 5.0V 5cm 1cm 2cm**Current conservation**I2 I1 I3 I1=I2+I3 I1 I3 I2 I1+I2=I3 Iin Iout Iout = Iin**Resistors in Series and parallel**R1 R2 • Parallel • V1 = V2 = V • Req = (R1-1+R2-1)-1 • Series • I1 = I2 = I • Req = R1+R2 I1+I2 I R1 R1+R2 I = = I1 I2 I R2 2 resistors in series: R L Like summing lengths**Quick Quiz**What happens to the brightness of bulb A when the switch is closed? Gets dimmer Gets brighter Stays same Something else**Quick Quiz**R1=200Ω R4=100Ω 9V R2=200Ω R3=100Ω 3V 6V Req=100Ω 9V Req=50Ω What is the current through resistor R1? 5 mA 10 mA 20 mA 30 mA 60 mA**Power dissipation (Joule heating)**• Charge loses energy from c to d. • Ohm’s law: • Energy dissipated in resistor as • Heat (& light) in bulb • Power dissipated in resistor = Joules / s = Watts Physics 208 Lecture 15**Capacitors as circuit elements**• Voltage difference depends on charge • Q=CV • Current in circuit • Q on capacitor changes with time • Voltage across cap changes with time**Capacitors in parallel and series**• ΔV1 = ΔV2 = ΔV • Qtotal = Q1 + Q2 Q1=Q2 =Q ΔV = ΔV1+ΔV2 1/Ceq = 1/C1 + 1/C2 Ceq = C1 + C2 Series Parallel**Example: Equivalent Capacitance**C1 C2 C3 V C4 C1 = 30 μF C2 = 15 μF C3 = 15 μF C4 = 30 μF in series Parallel combinationCeq=C1||C2**R**R RC Circuits C C ε Charge Discharge Time constant Start w/uncharged CClose switch at t=0 Start w/charged CClose switch at t=0**Question**R1=100Ω 10V C=1µF R2=100Ω What is the current through R1 Immediately after the switch is closed? A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A**Question**R1=100Ω 10V C=1µF R2=100Ω What is the current through R1 a long time after the switch is closed? A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A**Question**R1=100Ω 10V C=1µF R2=100Ω What is the charge on the capacitor a long time after the switch is closed? A. 0.05µC B. 0.1µC C. 1µC D. 5µC E. 10µC**RC Circuits**What is the value of the time constant of this circuit? A) 6 ms B) 12 ms C) 25 ms D) 30 ms**FB on a Charge Moving in a Magnetic Field, Formula**FB = q v x B • FB is the magnetic force • q is the charge • v is the velocity of the moving charge • B is the magnetic field • SI unit of magnetic field: tesla (T) • CGS unit: gauss (G): 1 T = 104 G (Earth surface 0.5 G)**Magnetic Force on a Current**S I • Force on each charge • Force on length of wire • Force on straight section of wire, length L Current N Magnetic force Magnetic field**dB**r ds r = distance from current element = permeability of free space Law of Biot-Savart B out of page • Each short length of current produces contribution to magnetic field. r I in plane of page ds Field from very short section of current Physics 208 Lecture 15**Magnetic field from long straight wire:Direction**r = distance from wire = permeability of free space y • What direction is the magnetic field from an infinitely-long straight wire? x I**y**x z Magnetic field from loop Bz A. z Which of these graphs best represents the magnetic field on the axis of the loop? Bz B. z I Bz C. z Bz D. z Physics 208 Lecture 15