A thin spherical shell of radius 15 cm carries 4.8 μC, distributed uniformly over its surface. At the center of the shell is a point charge. Part A If the electric field at (just barely outside) the surface of the sphere is 750 kN/C and points outward, what is the charge of the point charge?

Explanation:

It is known that on the surface of the shell the electric field will be the sum of electric field due to the shell and due to the point charge.

                =

Thus, we can conclude that charge of the point charge is .

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .