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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.)
How far east of his starting point will he reach the opposite bank? What is the magnitude of his velocity relative to the earth.
Speedboat A negotiates a curve whose radius is 124m. Speedboat B negotiates a curve whose radius is 230m. Each boat experiences the same centripetal acceleration. What is the ratio vA/vB of the speeds of boats.
A ball is thrown upward from the ground with an initial speed of 23.90 m/s; at = same instant, a ball is dropped from a building 16 m high. After how long will the balls be at the same height.
With what minimum speed should you toss a 140g ball straight up to hit the 11.0m-high roof of the gymnasium if you release the ball 1.30m above the ground? Resolve this problem using energy.
Two loudspeakers are vibrating in phase. They are set up as point C is located. Assume the speed of sound is 342 m/s. The speakers play the same tone. What is the smallest frequency that would produce destructive interference at point C.
A screen is placed 51.0 cm from a single slit that is illuminated with light of wavelength 677 nm. If the distance between the first and third minima in the diffraction pattern is 2.80 mm, what is the width of slit.
A football kicked off at an angle 20° from the ground reaches a maximum height of 4.7 m. What is the initial velocity of the kick.
A plane flies from base camp to Lake A, 280 km away in the direction 20° north of east. After dropping off supplies it flies to Lake B that is 190 km at 30° west of north from Lake A. Graphically find out the distance and direction from Lake B to ..
what force would be needed to pull the same wooden.
What is wavelength in meters of an electron
How several meters away is a cliff if an echo is heard 0.587 s after the original sound? Assume that sound traveled at 343 m/s on that day.
An asteroid is discovered heading straight toward Earth at 14 km/s . An international team manages to attach a giant rocket engine to the asteroid. The rocket fires for 10minutes , after which the asteroid is moving at 28degrees to its original pa..
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