Average emf induced in Square Loop

[connie5828]

Homework Statement

A square loop of side .45 m is placed in a region where there is a magnetic field of strength 8T directed perpendicularly out of the plane of the loop. If the magnetic field is increased to 14 T in .03 seconds, calculate the average emf induced in the loop

Homework Equations

A_i= w²=.45²
A_f=4*.45²/3.141
O_i=B_iA_icos (0)=
O_f=B_fA_fcos(0)
Eind= -(O_f-O_i)/time

The Attempt at a Solution

I tried doing the above and it isn't coming up with an answer that is even close to the choices I can choose from. Please help

 

[Redbelly98]

Homework Statement

A square loop of side .45 m is placed in a region where there is a magnetic field of strength 8T directed perpendicularly out of the plane of the loop. If the magnetic field is increased to 14 T in .03 seconds, calculate the average emf induced in the loop

Homework Equations

A_i= w²=.45²
A_f=4*.45²/3.141

A_i is correct, but what are you doing with A_f here? The area of the loop does not change in this problem.

O_i=B_iA_icos (0)=
O_f=B_fA_fcos(0)
Eind= -(O_f-O_i)/time

The Attempt at a Solution

I tried doing the above and it isn't coming up with an answer that is even close to the choices I can choose from. Please help

Your method looks correct, except for the confusion about A_f. Try it with the same area area for A_i and A_f, and show your full calculation if you need more help.

 

[aftershock]

Think of Faraday's law of induction.

You're going to need to find a function for the magnetic flux and take the derivative with respect to time.

The flux isn't going to take any crazy calculus here, it almost boils down to just BA, but B is not a constant.

B= B₀+ct where B₀ is the original field strength, c, is the rate at which it's increasing and t is the time.

so flux is (B₀+ct)A now see if you can derive and solve