A circular current‑carrying loop lies so that the plane of the loop is perpendicular to a constant magnetic field of strength B. Suppose that the radius R of the loop could be made to increase with time t so that R = at, where a is a constant. What is the magnitude of the emf that would be generated around the loop as a function of t ?

The magnitude of the emf  is  

Explanation:

Let  e be the magnitude of the emf that would be generated

    Since the loop is carrying current then there will be magnetic flux flowing through the loop area, let denote this magnetic flux as and can be mathematically represented as

Where B is the magnetic field

           A area of the loop

The change magnetic flux with time is mathematically represented as

  From this equation we see that the change of magnetic flux with time as changes the area with time

     Generally Area is mathematically represented as

From the question we are told that the radius  is

substituting this into the equation for A

Now the change of area with would be mathematically evaluated as

Given that since the plane of the  loop is  perpendicular to the constant magnetic field of strength B

   Now e can be represented mathematically as

Where N is the number of turns  = 1  that is a loop

substituting for change in area with time

explanation:

newton's third law, for every action there is an equal and opposite reaction.

12000j is work done