The magnitude of the electric field at a distance of two meters from a negative point charge is E. What is the magnitude of the electric field at the same location if the magnitude of the charge is doubled.

If the charge is doubled, the electric field is also doubled.

Explanation:

Electric field due to the negative charge is given as:

where k = Coulomb's constant

Q = electric charge

r = distance between charge and point of consideration

At 2 m from the negative charge, the magnitude of the Electric field due to a negative charge -Q is given as E:

If the charge is doubled, the new charge becomes -2Q and the new electric field becomes:

If the charge is doubled, the electric field is also doubled.

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 .