Aspherical shell in the region a ≤ r ≤ b carries a charge per unit volume of rho = a / r , where a is constant. at the center (r = 0) of the enclosed cavity is a point charge q. what should the value of a be so that the electric field in the region a ≤ r ≤ b has constant magnitude?

Explanation:

I will use the Gauss's Law to find the field:

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the surface S is a sphere of radio r, the normal vector only has radial coordinates.

E(r)=E(r)r /*The field, based on spherical symmetry, only depends of the radius, and only has radial coordinate*/

if r<a

if a=<r<b

with K=constant

none, its a machine

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.