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241_hw04

241_hw04 - Physics 241 Conductors Insulators and Capacitors...

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Unformatted text preview: Physics 241 - Conductors, Insulators and Capacitors 1: The current in a particular wire varies with time as I (t) = 1.5+ 375+ 21?2 amps. Determine the number of electrons that pass by a particular cross section in the wire between 5.9 and 73. 2: The current density in a cylindrical Wire of radius R is 5': jopl/R where i is a unit vector parallel to the wire and p is the cylindrical radial coordinate. Determine the total current in the wire. 321: You have a rectangular solid. You would like to pass current through it so that it has the least resistance. Should you direct the current perpendicular to side A, B, or C? Explain. b: In a different experiment, current is passed through side A (and out the opposite side). Use 0.2m x 0.1m x 0.02m for the dimensions of the solid and assume that the solid is made of copper so p = 1.69 X IO‘BQm and 123- = 8.49 x 102Be‘/m3. The potential! across the solid is maintained at 0.001V. Determine the drift velocity of the electrons and then how long it would take a single electron to pass completely through the copper. 4: Current passes through a piece of wire whose radius varies. How do the dirift velocity, the current density and the electric ﬁeld vary along the wire? Explain. ' 5: In class, we made a drawing of the electric ﬁeld and equipotentials around a spheri- cal conductor that was placed in an initially uniform electric ﬁeld. Change the drawing (qualitatively) to accommodate the sphere being a dielectric. Explain your modiﬁcations. 6: Two charges (q and —q) are a distance d = 0.1m apart. What value of qiwill produce an electric ﬁeld strength exactly halfway between the charges sufﬁcient to ionihe the air? The dielectric strength of air is 3 x 106V/m. i 7: You have GuF and Zn?” capacitors in a circuit with a 200V battery. a: The capacitors are connected in parallel (left ﬁgure). Determine the voltage drop across each capacitor and the charge on each capacitor. 3 b: Repeat part a: but now the capacitors are connected in series (middle ﬁgure). c: The two capacitors in part a are disconnected from the battery and fiom each other. They are then reconnected positive plate to negative plate and negative plate to positive plate. The right diagram shows the initial connections before the charge had time to move. Determine the ﬁnal charge on each capacitor and the voltage across each capacitor. Cl .tﬂﬁﬂt 8: You have a single capacitor connected to a battery. However, the tin plates on the capacitor do not have the same area. Does each plate still have the same charge? Explain. 9: In our derivation of the capacitance of a parallel plate capacitor, we assumed that E = 0/60. This is only correct if the plates are inﬁnitely large. Does our expression 0 = GoA/d underestimate or overestimate the true capacitance? Explain. 10a: In this circuit, 01 = SpF, 02 = 4:].LF, 03 = 4MP, C4 = GuF and V =5100V. Find the equivalent capacitance. ' b: Find the charge on each capacitor and the voltage across each capacitor; c: 02 suddenly shorts out so that it is effectively a conducting wire. What the new equiv- alent capacitance for the circuit? Explain. are 11: Two dzﬁerent capacitors 01 and 02 are connected in series (as in 7b). it possible that they are both storing the same amount of energy? Explain. 123: Find the equivalent capacitance between points A and B. Use CI = 6 'F, Cg = 1.5pF, C3 = 3/.LF, C4 = 3MF, Cs = and 05 = b: If 04 stores [10006.] of energy, determine the energy stored by the other} capacitors. c: Determine the potential difference between points A and B. C. CH 13: Determine the force that the two plates of a parallel plate capacitor exerEt on each other. Note: if you ﬁnd the quick way to do this problem, it will only take one line. 2 l l 14a: A parallel plate capacitor (of area A and separation distance d) is initially charged by a battery of voltage V and is then disconnected from the battery. A dielectric: of width L and dielectric constant fee is inserted into the capacitor (but doesn’t ﬁll all of the space). Does the charge on the plates change? Explain. You may assume that everything is essentially an inﬁnite plane. i b: Determine the new capacitance by using C = Q/AV. Does the expression give the correct results in the limit that L -—> O and L —> d? Explain. ‘ c: Determine the ratio of the ﬁnal energy stored to the initial energy stored. Does the expression give the correct results in the limit that L —> 0 and L —> d? Explain. d: Why doesn’t the exact location of the dielectric matter here? e: Imagine that you did not disconnect the battery in this problem. Would 'your answers to parts a, b or c change? Explain. i .- -.- ‘ 3.3083: ~ 0.0.0.4 “0.0.3.0‘ ‘o'o'o'o‘ i 0.... 4 ‘3'0'0'3‘ ’ C 0.. 90:. .1 9| .- a @3333: 15: A parallel plate capacitor is ﬁlled with two dielectrics (left image belovrlr). Explain why this can be viewed as two capacitors in parallel. Determine the capacitance. Note that this is deﬁnitely an approximation since the “capacitors” are not really isolated ﬁrom each other. 16: A capacitor (right image above) has square plates of side a. However; one plate is at a small angle relative to the other. Determine the capacitance for small 6.1 Note that this arrangement can be viewed as an inﬁnite series of parallel capacitors so you: can sum them (Le. integrate over them) to determine the capacitance. i ...
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