Work out the force due to the Miyamoto-Nagai disc potential.
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Work out the force due to the Miyamoto-Nagai disc potential.
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- Consider an “anti-gravity” potential (or, more mundanely, the electrostatic potential between two like charges), V(r) = α / r where α > 0. Show that circular, elliptical and parabolic orbits do not exist.A particle moves in a potential given by U(x) = -7 x3 + 2.1 x (J). Calculate the location of the stable equilibrium of this potential, in m. (Please answer to the fourth decimal place - i.e 14.3225)solve for the table , show work.
- find the potential function f for the field F=3xi+6yj+7zkA 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 stepConsider a particle of mass m acted upon by a central potential (r is distance and a>0 is a constant): U (r) p2 a) What are the constants of the motion? b) Is a circular orbit possible in this potential? If so, state the conditions for it. c) Under what conditions will the particle fall to the center of the potential (r = 0)?
- Consider a hollow sphere with radius R and surface potential V(0) = 5 – cos0. Use the general solution of Laplace equation V (r, 8) = E3 (A;r' +)Pi(cos®) to find an expression for the potential at any point outside the sphere. a) V(r,8) : R3 cose R3 cose 2R cose b) V(r, 8) 3R c) V(r,6) R3 R cose 4R 5R d) V (r, 8) - cose e) V(r,8) a b C d eA dielectric sphere in an external field. Consider a simple dielec- tric with permittivity e, in the form of a uniform spherical ball of radius a. It is placed at the origin in an external electrostatic potential (x, y, z) = bxy (where r, y, z are Cartesian coordinates and b is a constant). Find the elec- trostatic potential o and electric field E everywhere. %3DGive an example to show that a factor ring of an integral domain may be a field.