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A total charge of Q is deposited on a solid metal sphere of radius R. This charge distributes itself uniformly over the surface, yielding an electrostatic field E~ perpendicular =(sigma / e0) n^ just outside the sphere and E~ = 0 everywhere inside the sphere, where sigma = Q=4 pie R^2 and ^n is the outward pointing unit normal vector. Consider a small patch of surface area dA. We wish to calculate the electrostatic pressure P on this patch due to all the other surface charge. This pressure equals the electrostatic force per unit area, P = (dq)E=dA = sigma E where E is the electrostatic field acting on the patch due to all the other charges. But what value of E do we use? (The total fi eld is zero just inside the surface, but jumps to a nonzero value just outside the surface.) This problem addresses that question. a) Consider the small patch alone. What are the fi elds ~E ~patch that the patch produces just outside and just inside the sphere? (Write these fi elds as vectors involving sigma and ^n.) Hint: If you are in finitesimally close to the patch, even this small patch will look like an inf inite sheet of charge. b) According to the superposition principle, the total field just outside the surface must equal a contribution from the patch itself plus a contribution ~E ~other from all the other charge. What is ~E~other just outside the surface? (Again, write the result in terms of sigma and ^n.) c) In a similar manner, use the superposition principle to calculate the fi eld ~E~other just inside the surface. d) Is ~E~other continuous in both magnitude and direction as you move through the surface? e) What is the electrostatic pressure P on the patch due to all the other charges, in terms of sigma and e0? f) The largest E- fields that can be produced at the surface of a conductor are approximately 250 X 10^6 N/C. Beyond this value the metal breaks down due to fi eld emission. How much charge would have to be deposited on a sphere of copper 1 cm in radius to produce a field of this magnitude? What would the resulting electrostatic pressure be, in both N/m^2 and atmospheres? (1 atmosphere =101,325 N/m^2.)
A planet's moon travels in an approximately circular orbit of radius 6.6 x10^7 m with a time of 7 h 9 min. Calculate the mass of the planet from this information.
A car accelerates uniformly from rest and covers a distance of 71 m in 5.6 s. If the diameter of a tire is 42 cm, 1.) Find the angular acceleration of the wheel.
Outline what you know about Plasmonics? Outline what you know about Raman spectroscopy and surface enhanced Raman spectroscopy?
How long would it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 324.
When the wire is removed, the spheres repel each other with an electrostatic force of 0.0394 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive cha..
A rifle with a barrel length of 56 fires an 8 bullet with a horizontal speed of 350. The bullet strikes a block of wood and penetrates to a depth of 14. (a) What resistive force (assumed to be constant) does the wood exert on the bullet? (b) How long..
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What must be the temperature of the cold reservoir in order to increase the efficiency to 29.0%
An air parcel moves northwards and becomes entrained in a strong westerly flow, circling the entire globe in the space of a few weeks. State the name given to this high-level flow and define briefly how its structure is related to lateral and vert..
What's the result when we grow up InGaN on the substrat by MBE I want a (pdf) discruption or I want to talk to any one who knew that's result.
A container of hot water at 50 degrees cools to 49 degrees in how many seconds when it is placed in a room that is t 20 degrees. use newton's law of cooling to find the time it will take for the container to cool from 50 degrees to 49 degrees.
What is the vertical force on the support closest to the piano.
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