1. A non-conducting, thin, spherical shell of radius g is maintained with a potential Q=V, cos on its surface. a. Find the electric potential as a function of position, both inside and outside the sphere.
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- 123. A thin circular ring has a radius R and charge3 Q distributed uniformly over its length. What is the electric potential at the center of the ring? Hint: this is very easy since every point on the ring is the same distance from the center. Therefore you don't need to integrate. а. 3Q, R b. What is the electric potential at a distance z along the axis of the thin ring? Comment: each point on the ring is still the same distance from point P. 3Q, R1. A disk of radius R has positive charge Q distributed uniformly across its surface. The disk lies flat in the xy-plane, and the z-axis intersects the disk at its center. Z Q x y (a) Determine the electric potential at all points on the z-axis. Assume that the potential goes to zero infinitely far away from the disk. (b) From the potential you found in Part (a), determine the electric field at all points on the z-axis. Make sure that your electric field points in the correct direction above and below the disk.
- B99. An electron has been placed at the origin. The grid spacing is 1 Angstrom per small square this time. Now you have a nucleus with 12 protons at x = 4.0 Angstroms on the x-axis. What is the value of the electrostatic potential V at a point on the positive y-axis, at y = 7.1 Angstroms? 21.2 V 11.5 V 19.2 V -2.0 VB1
- 1. Find the electric potential at a distance r from the center o of a spherical shell of radius R with charge Q distributed uniformly on the surface of the shell. Consider both cases: r R. Q R12. The electric potential generated by a uniformly charged disk of total charge Q and radius R is given by 20 F(y) = (Vy² + R² – y), - where y is the distance from the disk and F(y) is the potential at distance y. We want to understand what happens when y is very large, so do this: a. Change variables from y to x = 1/y, so that when y is big, x is close to zero. Simplify! b. Find a Taylor polynomial centered at x = 0 for the potential in terms of x. c. Use this to justify the following claim: "at points far from the disk, the po- tential is approximately Q/y."4. Conductive sphere with charge. A solid conducting sphere of radius R has a total charge q. Find the potential in all places, both outside and inside the sphere.
- 4. Figure below shows a ring of outer radius R = 13.0 cm, inner radius r= 0.200R, and uniform surface charge density o = 6.20 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.0OR from the center of the ring. %3D R2. A conducting sphere with radius R and total charge Q is centered at the origin. The space outside the sphere above the z = 0 plane has relative permittivity K₁. The space outside the sphere below z = 0 has relative permittivity K₂. a) Find the potential everywhere outside the sphere. b) Find the surface charge distribution on the surface of the sphere. ZA Thin