Question

Problem 10b

Answer 1

Given information

A circular loop in the plane of the paper.

The magnetic field is   pointing into the paper.

The resistance of the coil is .

The diameter changes in  

Step-by-step explanation

Step 1.

Calculate the flux through the circular loop by using formula

 

Here,   is the magnetic field,   is the area of the circular loop, and  is the angle between the magnetic field and the area vector.

The area of the circular loop is , that is,

 

Here,   is the radius of loop.

The relation between the radius and the diameter is

 

Here,  is the radius and  is the diameter.

Therefore, the expression for the flux is rewritten as

 

Therefore,

 

The expression for the induced  is

 

Here, is the change in the flux,  is the number of turns, and is the change in time.