A non-charged infinitely wide plate conductor is parallel to andhas a distance from an infinitely wide plane of charge with surfacecharge density ?. Find the electric field in regions 1 to 4 (seefigure below). (note, no need to use the Gaussâ Law).

Also,

Just write down the major equations in Problem 4 if the infinitelywide plate conductor carries a net charge of +Q (you can assumethat the surface has an area A, even though it is very large. Noneed to do calculations).

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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) Two pith balls each of mass m and carrying charge q aresuspended
from the same point by insulating threads of length L. Findan
expression for the angle each string makes with the vertical.

b) A pith ball of mass m and carrying a charge q is attached to thecenter
of a very large vertical insulating sheet carrying a uniformsurface
charge density s by an insulating thread of length L. Find an
expression for the angle the string makes with the plane.

c) A pith ball of mass m and carrying a charge q is positioned adistance
D from a very large conducting plane. For what value of D wouldthe
electric force on the ball be the same magnitude as in parta)?

d) For each of the three cases above, sketch the total electricfield

everywhere to the left of the plane

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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

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