Consider a point charge q inside a grounded (empty) metallic shell. from radius to. Calculate the electrostatic potential inside the shell and the induced charge density on it. this one on the inside wall. What is the value of the total induced charge?
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- Check Your Understanding How would the above limit change with a uniformly rectangle instead of a disk?Discuss the restrictions on the Gaussian surface used to discuss planar symmetry. For example, is its length important? Does the cross-section have to be square? Must the end faces be on opposite sides of the sheet?What is the magntiude of the integral of B over dl for part b? Enter in your answer in micro-T*m. Assume that all currents are 19.2 A instead of what the textbook has noted.
- What is the magntiude of the integral of B over dl for part c? Enter in your answer in micro-T*m. Assume that all currents are 14.7 A instead of what the textbook has noted.Charge is distributed throughout a very long cylindrical volume of radius R such that the charge density increases with the distance r from the central axis of the cylinder according to p=ar , where a is a constant. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E=ar230 (rR); E=aR330r (rR).Suppose a piece of infinite length. We have the surface density of Sigma, which has width a, find the field at distance z؟
- A total charge Q is distributed uniformly throughout a spherical shell of inner and outer radii r1 and r2 , respectively. Show that the electric field due to the charge is E =Q40r2(r3r13r23r13)r (rr1); (r1rr2); E =Q40r2r (rr1).The conductor in the preceding figure has an excess charge of 5.0C . If a 2.0C point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. We willcalculate the exact field due to the rod in the next homework set. In this set, we will approximatethe rod as several point sources and develop the Riemann sum as an intermediate step on the wayto writing an integral.For those aiming at a P rating, you may use L = 3.0m , Q = 17 mC, and y = 0.11m to calculate theanswer numerically first and substitute variables for them only as required in the problem statement.For those aiming at an E rating, leave L, Q and y as variables. Substitute numbers only whererequired in the problem statement, and only as a last step
- A particle of charge q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=12qQ40mR3.Consider a point charge 3Q is located at the origin. Divergence of the electric fluxdensity produced by the charge isCalculate the potential energy of the interaction between two linear quadrupoles when they are parallel and separated by a distance r.