5/18/11 1 Physics 122 Theme Music: Duke Ellington Take the A Train Cartoon: Bill Amend FoxTrot May18, 2011 Physics 122 Prof. E. F. RedishReview sheets for Final Exam Material from two previous exams plus Electric currents – Definition of currents – Basic principles (Kirchoffs Laws) Capacitors Basics of Magnetism and Electromagnetism – (Very little – just the idea) 5/18/11 2 Physics 122Previous Exam Results #1 #2 #3 #4 #5 Exam 1 64% 80% 86% 47% 79% Exam 1 (MU) 51% 60% 67% 82% 44% Exam 2 76% 77% 27% 64% 73% Exam 2 (MU) 74% 55% 43% 26% 53% 5/18/11 3 Physics 122Quiz Results 5/18/11 4 Physics 122 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 1 90% 16% 98% 71% 73% 76% 76% 80% 22% 90% 93% 2 76% 26% 41% 67% 66% 83% 67% 8% 84% 83% - 3 43% 50% 63% 55% 31% 39% 63% 41% 73% 40% 37% 4 43% 41% 76% 58% 12% 5 41%5/18/11 5 Physics 122 How Much Current? If there is a density of electrons n per unit volume and they are moving with a velocity v, then how many cross the surface in a time Δt? Δx = v Δt Volume = AΔx N = (no. density) x (volume) = nAv Δt I =(charge crossing A)/(time) = qN/Δt = qnAv Δx = v Δt v A n5/18/11 6 Physics 122 Foothold ideas: Currents Charge is moving: How much? How does this relate to the individual charges? Constant flow means pushing force balances the drag force What pushes the charges through resistance? Electric force implies a drop in V! tqIΔΔ=I = q n A v ma = Fe− bva = 0 ⇒ v =FebFe= qEΔV = −EL5/18/11 7 Physics 122 Ohms Law Current proportional to velocity Due to resistance, Electric force proportional to velocity. Force proportional to electric pressure drop = electric PE Therefore, current proportional to electric PE IRV =ΔI = qnAv ⇒ v =IqnA qE = bvΔV = EL ⇒ E =ΔVL⇒qΔVL=bIqnAΔV = IbLq2nA⎛⎝⎜⎞⎠⎟≡ IR5/18/11 8 Physics 122 Electric circuit elements Batteries —devices that maintain a constant electrical pressure difference across their terminals (like a water pump that raises water to a certain height). Resistance —devices that have significant drag and oppose current. Pressure will drop across them. Wires — have very little resistance. We can ignore the drag in them (mostly – as long as there are other resistances present).Resistivity and Conductance The resistance factor in Ohms Law separates into a geometrical part (L/A) times a part independent of the size and shape but dependent on the material. This coefficient is called the resistivity of the material (ρ). Its reciprocal (g) is called conductance. 5/18/11 9 Physics 122 R =bLq2nA⎛⎝⎜⎞⎠⎟=ρLA=1gLA5/18/11 10 Physics 122 Foothold ideas: Kirchoffs Rules Flow Rule – The total amount of current flowing into any point in a network equals the amount flowing out (no significant build-up of charge anywhere). Loop Rule – Following around any loop in an electrical network the potential has to come back to the same value (sum of drops = sum of rises). Ohms Rule – When a current I passes through a resistance R, there is a voltage drop across the resistor of an amount Battery rule – A battery provides a constant ΔV across its terminals. Constant Potential Trick – Along any conducting part of a circuit with 0 resistance, V = constant. IRV =Δ5/18/11 11 Physics 122 Foothold ideas: Power Power is defined as the rate of (delivering or using) energy. The unit of power is the Watt (= 1 J/s = 1 Amp-Volt). In a battery or resistor, the power is P =ΔWΔt=F ⋅ΔrΔt=F ⋅vP = IΔV5/18/11 12 Physics 122 ΔV = ΔVA+ ΔVBIReff= IRA+ IRBReff= RA+ RBI = IA+ IBΔVReff=ΔVRA+ΔVRB1Reff=1RA+1RBSeries and Parallel Rules In series, the current (I) through each element is the same. In parallel, the pressure drop (ΔV) across each element is the same. A B A B5/18/11 13 Physics 122 Storing electrical energy: The capacitor Two parallel metal plates of area A separated by a distance L. Connect the plates to the two sides of a battery. – – – – – – – + + + + + + + ΔV E L5/18/11 14 Physics 122 Capacitor Equations ΔV = EΔx = ELE = 4πkCQA⇒ Q =A4πkC⎛⎝⎜⎞⎠⎟EQ =A4πkCL⎛⎝⎜⎞⎠⎟ΔVVCQ Δ=C is measured in Coulombs/Volt = Farads 4πkc is often written as 1/ε0Capacitors: Foothold ideas 5/18/11 15 Physics 122 Although local neutrality is almost always true, various configurations support local charge separations. Such separations are always associated with electric fields and hence with potential differences. The ratio of the charge separation to the potential difference is the capacitance. Charge separations take work to create and are associated with stored energy. EΔx = −ΔVQ = CΔVΔU =12QΔV5/18/11 16 Physics 122 Dielectrics If an insulator is put between the plates, there is still some polarization reducing the field (by a factor of κ) so the voltage required for a given charge is reduced, i.e., C is increased. (Assuming the space between the plates is filled by the insulator.) C =κ14πkCALFoothold ideas: Phenomenology of Magnets 5/18/11 17 Physics 122 Certain objects (magnets) attract and repel other magnets depending on orientation. Magnets (all orientations) attract a certain class of other objects – iron, steel,… but not all metals (e.g., aluminum, copper,…). Objects that are attracted by magnets can be made into magnets by being stroked consistently in one direction with a magnet. Magnets can lose their magnetism by heating or hammering.. Each part of a broken magnet still shows attraction and repulsion with other magnets.Foothold ideas: Magnetism 2.0 Magnetic fields are produced by magnets and by moving charges (currents). Magnetic fields are felt by magnets and by moving charges (currents). Magnetic force law: Magnetic field law: Although there are magnetic dipoles (e-, p+) there are no separate magnetic poles. 5/18/11 18 Physics 122 FB= qv ×B ΔF = IΔL ×B ΔB = kAIΔL ׈rr25/18/11 19 Physics 122 Maxwells Principles Maxwell 1: Point charges serve as sources to create electric fields.
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