PHYS 2305 Lecture Notes - Lecture 9: Farad, Electric Field, Potential Energy

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scarlethare218

17 Nov 2015

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Capacitance: any two conductors separated by an insulator form a capacitor, when electrons are transferred from 1 conductor to another, it charges it. The two charged conductors have charges with equal magnitude: the unit for capacitance is farad (f, capacitance is the ability of a capacitor to store energy. C=q/vab: c- capacitance, q- charge, vab- potential difference, parallel plate capacitors consist of two conducting plates with an area, separated by a distance, the field between parallel plate capacitors is uniform, and the charges are uniformly distributed. E= / 0: e- electric field magnitude, - absolute value of the surface charge density on each plate. 0- 8. 85e-12: c- capacitance of a parallel plate capacitor in a vacuum, a -area of plate, d- distance of separation. Capacitors in parallel: voltage across all capacitors is the same, net charge= q1+q2+q3 , capacitance= c1+c2+c3 . Capacitors in series: voltage= v1+v2+v3 , net charge is the same across all capacitors, capacitance= (1/c1)+(1/c2)+(1/c3) .

Related Questions

To understand the meaning of capacitance and ways of calculating capacitance.

When a positive charge q is placed on a conductor that is insulated from ground, an electric field emanates from the conductor to ground, and the conductor will have a nonzero potential V relative to ground. If more charge is placed on the conductor, this voltage will increase proportionately. The ratio of charge to voltage is called the capacitance C of this conductor: C=q/V.

Capacitance is one of the central concepts in electrostatics, and specially constructed devices called capacitors are essential elements of electronic circuits. In a capacitor, a second conducting surface is placed near the first (they are often called electrodes), and the relevant voltage is the voltage between these two electrodes.

This tutorial is designed to help you understand capacitance by assisting you in calculating the capacitance of a parallel-plate capacitor, which consists of two plates each of area A separated by a small distanced with air or vacuum in between. In figuring out the capacitance of this configuration of conductors, it is important to keep in mind that the voltage difference is the line integral of the electric field between the plates.

Assume that charge -q is placed on the top plate, and +q is placed on the bottom plate. What is the magnitude of the electric field E between the plates?
What is the voltage V between the plates of the capacitor?

beigemouse1

This has been bothering me for a long time and I cant find anadequate explanation..

Lets say you have an infinite conducting plate with finitethickness D and it is given charge Q

the charge will be equally split into two and concentrated only onthe two surfaces.

Each surface will get Q/2

and the magnitude of electric field outside the plate isE=Q/(2A*epsilon naught) (E for a conducting plate is surface chargedensity/epsilon naught as opposed to surface chargedensity/(2epsilon naught)

Then, if you have two nonconducting plates separated by distance Dand each plate gets Q/2 which is uniformly distributed ..
then outside the space between the two plates, E = 2*(Q/4A*epsilonnaught)

But why cant we use superposition principle in the case of oneconducting plate with Q and say you get E=Q/(A epsilon naught)i.e.Q/(2A epsilon naught) from each surface...

Is it because we are looking at the mid section of the conductor assome kind of Faraday cage? (since the plate is essentially infinityand blocks the electric field from the other side?)

Also, lets look at two parallel plate capacitor..

One plate gets +Q/2 and the other gets -Q/2

I know the formula says E= charge density/epsilon naught.. so E hasto be Q/(2A epsilon naught) However, it seems rather inconsistentin the case of the parallel plate capacitor...

We know all the charge is going to be concentrated on the innersurface
So shouldnt you get E = Q/(2A epsilon naught) solely from one plateand since you have TWO plates!!!, shoudlnt you multiply Q/(2Aepsilon naught) by 2?

A magnetic field of 0.1T forces a proton beam of 1.5 mA to move ina circle of radius 0.1 m. The plane of the circle is perpendicularto the magnetic field.

47. Of the following, which is the best estimate of the speed of aproton in the beam as it moves in the circle?
(A) 10-2 m/s (B) 103 m/s (C) 106 m/s (D) 108 m/s (E) 1015 m/s

52. An ideal gas is initially in a state that corresponds to point1 on the graph above, where it has presÂ¬sure p1, volume V1, andtemperature T1. The gas undergoes an isothermal process representedby the curve shown, which takes it to a final state 3 attemperature T3. If T2 and T4 are the temperaÂ¬tures the gas wouldhave at points 2 and 4, respecÂ¬tively, which of the followingrelationships is true?
(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 =T4

53. The absolute temperature of a sample of monatomic ideal gas isdoubled at constant volume. What effect, if any, does this have onthe pressure and density of the sample of gas?
Pressure Density
(A) Remains the same Remains the same
(B) Remains the same Doubles
(C) Doubles Remains the same
(D) Doubles Is multiplied by a factor of 4
(E) Is multiplied by a factor of 4 Doubles

62. A sample of an ideal gas is in a tank of constant volume. Thesample absorbs heat energy so that its temperature changes from 300K to 600 K. If v1 is the average speed of the gas molecules beforethe absorption of heat and v2 is their average speed after theabsorption of heat, what is the ratio v2/ v1 ?
(A) 1/2 (B) 1 (C) (D) 2 (E) 4

63. Two people of unequal mass are initially standing still on icewith negligible friction. They then simulÂ¬taneously push each otherhorizontally. Afterward, which of the following is true?
(A) The kinetic energies of the two people are equal.
(B) The speeds of the two people are equal.
(C) The momenta of the two people are of equal magnitude.
(D) The center of mass of the two person system moves in thedirection of the less massive person.
(E) The less massive person has a smaller initial acceleration thanthe more massive person.

64. Two parallel conducting plates, separated by a distance d, areconnected to a battery of emf e. Which of the following is correctif the plate separaÂ¬tion is doubled while the battery remainsconnected?
(A) The electric charge on the plates is doubled.
(B) The electric charge on the plates is halved.
(C) The potential difference between the plates is doubled.
(D) The potential difference between the plates is halved
(E) The capacitance is unchanged.

68. A rod on a horizontal tabletop is pivoted at one end and isfree to rotate without friction about a vertical axis, as shownabove. A force F is applied at the other end, at an angle ? to therod. If F were to be applied perpendicular to the rod, at whatdistance from the axis should it be applied in order to proÂ¬ducethe same torque?
(A) L sin ? (B) L cos ? (C) L (D) L tan ? (E) L

70. A 4 ÂµF capacitor is charged to a potential differÂ¬ence of 100V. The electrical energy stored in the capacitor is
(A) 2 x 10-10 J (B) 2 x 10 8 J (C) 2 x 10 6 J (D) 2x 10-4 J (E) 2 x10-2 J

PHYS 2305 Lecture Notes - Lecture 9: Farad, Electric Field, Potential Energy

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