Induced current in copper wire

[vigintitres]

Homework Statement

A square loop, 5.3 m on a side, is made of copper wire, 0.9 mm in radius. A 3.2 T magnetic field, perpindicular to the loop is increasing at the rate of 0.29 T/s. The resistivity of copper is 1.7 x 10^-8 ohm*m. Find the induced current. Answer in units of A.

Homework Equations

I'm assuming I need to use Faraday's law where I = V/R = magnetic flux/resistivity * time

The Attempt at a Solution

What actually threw me was the fact that the loop has a radius. So the area can't just be 5.3 squared and I don't think I need to calculate the area of a cylinder? Well I tried finding the initial value for the magnetic field then subtracting that from the final value after 1 second since it increases .29 T/s. I was just getting large answers and I can tell they would be somewhat large due to the large value of B, but I'm honestly stuck on how to set this beast up correctly.

 

[alphysicist]

Hi vigintitres,

Homework Statement

A square loop, 5.3 m on a side, is made of copper wire, 0.9 mm in radius. A 3.2 T magnetic field, perpindicular to the loop is increasing at the rate of 0.29 T/s. The resistivity of copper is 1.7 x 10^-8 ohm*m. Find the induced current. Answer in units of A.

Homework Equations

I'm assuming I need to use Faraday's law where I = V/R = magnetic flux/resistivity * time

The Attempt at a Solution

What actually threw me was the fact that the loop has a radius. So the area can't just be 5.3 squared and I don't think I need to calculate the area of a cylinder? Well I tried finding the initial value for the magnetic field then subtracting that from the final value after 1 second since it increases .29 T/s. I was just getting large answers and I can tell they would be somewhat large due to the large value of B, but I'm honestly stuck on how to set this beast up correctly.

The loop doesn't have a radius; the wire has a radius. This problem has several parts, and one part will require the area of the loop, and another part will use the cross sectional area of the wire.

So to answer your question. the area of the loop is just the area of a square. Does that help?

 

[vigintitres]

yes, thanks that will get me started at least. Am I correct that I am going to use Faraday's law and was the method of finding the initial B and the final B and subtracting the difference ok for this problem?

 

[alphysicist]

yes, thanks that will get me started at least. Am I correct that I am going to use Faraday's law and was the method of finding the initial B and the final B and subtracting the difference ok for this problem?

That should work for that part of Farday's law; or you could leave it as a derivative.