Solenoid flux-emf-current problem

[crbnmnxd3]

Homework Statement

A solenoid inductor has an emf of 0.20 V when the current through it changes at the rate 10.0 A/s. A steady current of 0.10 A produces a flux of 5.0 microWb per turn.

The number of loops in the solenoid is the value which needs to be found.

Homework Equations

The Attempt at a Solution

I have been going through this problem for a good hour, and am simply stuck. Clearly there are two different cases which are presented for the same solenoid, which clearly means that each case needs to be plugged into an equation and these two equations must be related through an unknown variable. Please state any equations you may use in the solving of this problem, I have two pages of fruitless work in front of me.

 

[rock.freak667]

$$\phi=BA$$

$$B= \frac{\mu NI}{l}$$

N=No. of turns
l=length.

You'll need those 2.

 

[crbnmnxd3]

The problem I keep running into with the first equation you listed is that I do not know what the radius of the solenoid is, and as a result I am unable to determine the surface area of the solenoid.

 

[rock.freak667]

Combining the 2 equations you'll get

$$\phi = \frac{\mu NIA}{l}$$


Dividing both sides by N


$$\frac{\phi}{N}=\frac{\mu IA}{l}$$

Can you use the second line of the question to find a value for the ratio of $\frac{A}{l}$?


Then use the fact that

$$E=\frac{d}{dt}{\phi}$$

or simply

$$E=\frac{\phi}{t}$$