What is the Inductance of a Coil with Changing Magnetic Field and Current?

[JDiorio]

Homework Statement

An inductor has the form of a coil with 2074 turns and a diameter of 1.9 mm . The inductor is placed in a magnetic field perpendicular to the plane of the coil and increasing at a rate of 0.48 T/s . The current in the inductor is zero at t = 0, and then increases to 6.9 mA at t = 1.0 s. What is the inductance?

Homework Equations

This is the problem, I am obviously missing something.
I want to use the equation L= (u*N^2*A)/length.. but as you can see I am not given the length. I do not know how to incorporate the charge into finding the inductance.

The Attempt at a Solution

I feel like I am close. I am trying to use the increase rate of the magnetic field to find the emf, and then use the emf and the current to find the inductance, but then i get stuck.

 

[JDiorio]

So I found the formula emf= -L ( dI/dt) where d = change in. How do I derive the emf from the information given. Also, this formula does not involve the number of turns nor does it involve the diameter.. so is this just extra information?

 

[rl.bhat]

You can the equation as
emf = - NAdB/dt = L*di/dt. Or
NA(dB/dt)*dt = L*di
Take integration on both side and find L.

 

[JDiorio]

is there anyway to do this problem without calculus? This is a non-calc based class so i have no clue how i would go about taking the integral..

 

[rl.bhat]

is there anyway to do this problem without calculus? This is a non-calc based class so i have no clue how i would go about taking the integral..

In the given problem, dt is given(1s). di is given(6.9 mA). Substitute in the formula to get the inductance. No need to take integration.

 

[JDiorio]

thanks a lot.. i finally got this stupid question.. really appreciate the help! thanks again..