Question

1. Parallel plates. You have two equal but oppositely charged parallel conducting plates, separated by 10 cm. A voltmeter shows that the potential difference between the plates is 500 V. (a) Which is at a higher potential, the positive or negative plate? (b) How big is the electric field between the plates? (c) You let go of an electron next to the negative plate. How much work does the electric field do in moving the electron to the positive plate? Expre your answer in eV as well as J. (d) What was the change in the electron's potential energy in part (c)? (e) What are the kinetic energy and speed of the electron when it reaches the positive plate? Point charges. An aluminum (Ali ) ion is located at origin, and an oxide (O) ion is located at x = a on the x-axis (a) Sketch a graph of the potential V(x) as a function of χ (by hand is fine. Just be neat). (b) where, if anywhere, does V = 0 on the x-axis? (c) Where, if anywhere, does the electric field E = 0 on the x-axis? Are these places, if any, the same as the ones where V0 in part (b)? Explain why or why not. (d) How much work would you have to do to place a proton at x-a/2? [Hint: work done change in potential energy. Treat the proton as starting at x-o] Relationship between potential and field the third is on the x-axis at x = a. (a) Find an expression for V(x) as a function of x, (b) Use your answer in part (a) to find an expression for Ex(x), the x-component of the electric field as a function of x. (c) Show that your answers to parts (a) and (b) reduce to the expected expressions when = 0 and when x » a 2. 3. . You have three identical charges q. Two are on the y-axis at y = ±a and 4. Continuous charge distribution (finding V from the point-charge formula V-kda/r). A uniformly charged rod lies along the y-axis with its center at origin. It has a total charge Q and length L. (a) Find an expression for V(x) as a function of x. (b) Show that your answer in part (a) reduces to the expected form when x LHint: For part (b) you can use two extremely useful formulas, called Taylor series approximations. These tell you that (1 + ε)" ~ 1 + pe for any power p when ε is small, and that ln(1 + ε)s ε when ε is small.] Continuous charge distribution (finding V from the definition V = field outside a long, uniformly charged wire is given by E = (2kλ/r)f where λ is the linear charge density. (a) Use this result to find the potential difference AV = V(r) -V(%) between two different distances r and Yo from the wire (b) Apply your result to a Geiger counter, which is a cylinder of diameter 4 cm containing a charged wire of diameter 0.5 cm along its central axis. Suppose the potential difference between the outer edge of the wire and the inner surface of the cylinder is 1 kV, and the cylinder is grounded (so that its potential is zero). How far is the 500 V equipotential surface from the wire? Is it midway between the wire and the cylinder? Explain. Hint: use the difference between the potential on the wire and the cylinder to find Electrostatic potential energy of a system of charges. You place four charges at the corners of a square that is centered at origin, as follows: +q is at (-a, +a), +2q is at (+a, +a), -3q is at (+a,-a), and +6q is at (-a,-a). (a) What is the electrostatic potential energy at origin? (b) If you put a fifth particle of mass m and charge q at origin and let it go, how fast will it be moving when it has receded to infinity? (c) Find a numerical value for your answer in part (b), assuming that q = e and a 1 pm. 5. . de). Recall from class that the electric 6.

Answer 1

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1.

a)

negative plate

b)

Electric field

E=V/d=500/0.1=5000 V/m

c)

Work done by electric fieldto move the electron to positive plate is

W=qV =(1.6*10^-19)(500)=8*10^-17 J

in eV

W=(8*10^-17)/(1.6*10^-19)=500 eV

d)

Change in electric potential energy

dU =500 eV or 8*10^-17J

e)

Kinetic energy

K=8*10^-17J

since K=(1/2)mv²

8*10^-17=(1/2)*(9.11*10^-31)*v²

v=1.325*10⁷m/s