Determine the general solution of the 1-dimensional Laplace equation on the cylinder coordinates and ball coordinates!
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Determine the general solution of the 1-dimensional Laplace equation on the cylinder coordinates and ball coordinates!
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- Suppose that we want to solve Laplace’s equation inside a hollow rectangular box, with sides of length a, b and c in the x, y and z directions, respectively. Let us set up the axes so that the origin is at one corner of the box, so that the faces are located at x = 0 and x = a; at y = 0 and y = b; and at z = 0 and z = c. Suppose that the faces are all held at zero potential, except for the face atz=c,onwhichthepotentialisspecifiedtobeV(x,y,c)=V0 =const. a) Find the electrostatic potential V at a generic point inside the box.b) Find the expression for the electrostatic potential evaluated at the center of the box, i.e. deter- mine V (a/2, b/2, c/2). Simplify your answer as much as you can! c) Suppose now that a = b = c, i.e. the box is a cube. Give a simple argument which gives theexact (and simple) expression for the potential at the center of the cube. (No calculations are asked here. Use physics, wave your hands, etc. and say “the answer is such and such because ...”)Convert the point from rectangular coordinates to cylindrical coordinates. (9sqrt3, -9, 6)Explain Laplace correction.
- A particle of mass m under the action of a central force describes an orbit that is a circle of radius a passing through the center of force. Find the law of force.help me answer part b, thank youProve that there is no work done by the Coriolis pseudoforce acting on a particle moving in a rotating frame. If the Coriolis pseudoforce were the only force acting on a particle, what could you conclude about the particle’s speed in the rotating frame?