A uniform magnetic field vector B is directed out of the page. A loop of wire of area 0.8 m2 is in the plane of the page. At a certain instant, the field has a magnitude of 5.0 T and is decreasing at the rate of 0.5 T/s. The magnitude of the induced emf in the wire loop at this instant is most nearly:

0.4 V

Explanation:

Given

The area of the loop is

The magnetic field is changing at the rate of

Induced EMF is given by

The magnitude of induced emf is 0.4 V

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 .