A surface of revolution is formed by rotating the function y = – about the x axis. Suppose youwere to take the portion of this surface that is in the domain that goes from x=a to x=+∞ andturn it into an electrical conductor, and then place a finite charge +Q onto it. Once the conductorattains electrostatic equilibrium, how would its final surface charge density vary as Q is varied?O The surface charge density is always undefined, independently of how Q is variedO It varies in direct proportion to Q in the region where x A bolt of lightning is associated with the motion of what type of charge?O the phenomenon of lightning is unrelated to the motion of electric chargeO a 50-50 mix of negative and positive chargeO predominantly positive chargeO predominantly negative charge

Bolt of lightning is associated with the motion of

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University Physics Volume 2

18th Edition

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Chapter6: Gauss's Law

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Problem 58P: Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed...

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Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2 , respectively. They are separated at center-to-center distance a (see below). Find the electric field at point P located at a distance r from the center of sphere 1 and is in the direction from the line joining the two spheres assuming their charge densities are not affected by the presence of the other sphere. (Hint: Work one sphere at a time and use the superposition principle.)
At the surface of any conductor in electrostatic equilibrium, E=/0. . Show that this equation is consistent with the fact that E=kq/r2 at the surface of a spherical conductor.
A standard coaxial cable consists of a cylindrical central conducting wire, a layer of surrounding insulation, a flexible conducting pipe-like sheath, and a final outer layer of insulation as shown in the figure. Imagine a very long straight stretch of such a wire, and suppose that the inner wire has a charge per unit length of λ and the sheath has a charge per unit lenth of -λ (where λ is a positive constant). a. Argue that the charge must reside in thin layers on the wire's outer surface and the sheath's inner surface. b. Determine Evector (in terms of R, λ, and ε0) in the regions (1) s < R, (2) R < s < 2R, and (3) s > 2R. c. Draw a quantitatively accurate graph of Er as a function of s from s = 0 to s = 3R. The graph will look discontinuous in places. Explain why this does not violate the continuity principle.
Calculate the electric field at point P for a thin nonconducting rod of finite length L with a charge q spread uniformly along it.
Determine the total charge distribution on r = b, and on r = a., explain Check if the electrical field for this configuration match the findings that for all points r inside the circle r<a is E= q/4piΕor2 and for all points r outside the shell r>a is E=0
Consider a conductor with total charge of −12q. The conductor has a cavity, and there is a+15q charge inside the cavity. How much charge is on the outer surface of the conductor?
A solid conductor carries a net positive charge −?. There is a hollow cavity within theconductor, at whose center is a negative point charge −?. What is the charge on:i. The inner surface of the conductor’s cavity? ii. The outer surface of the conductor?
Find the electric field a distance z above the midpoint of a straight line segment of length 2L, which carries a uniform line charge A.
A solid insulating plastic sphere of radius a carries atotal net positive charge 3Q uniformly distributed throughout its interior.The insulating sphere is coated with a metallic layer of inner radius a andouter radius 2a. The conducting metallic layer carries a net charge of -2Q. Apply Gauss’s law to find the magnitude of the electric field in the region r < a. Inthe figure, draw the Gaussian surface you are using, and indicate on that surface the direction of anyvectors which appear in the mathematical expression of Gauss’s law. Express your answer in terms ofa, Q, r, and ε0. (If you get an expression involving ρ, substitute it from above to re-express youranswer in terms of the stated variables.)
Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?
Examine the summary on page 780. Why are conductors and charged sources with linear symmetry, spherical symmetry, and planar symmetry categorized as special cases rather than major concepts or underlying principles?
Under electrostatic conditions, the excess charge on a conductor resides on its surface. Does this mean that all the conduction electrons in a conductor are on the surface?

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A bolt of lightning is associated with the motion of what type of charge? O the phenomenon of lightning is unrelated to the motion of electric charge O a 50-50 mix of negative and positive charge O predominantly positive charge O predominantly negative charge