Magnetic field at the center of a solenoid?

[tabitha2232]

A studetn needs to make a solenoid that produses 1.09 T at its center. a wire will be wrapped around a solid cylinder of iron with a relative permeability Km of 1400, a length of 13.3 cm and a radius of 1.92 cm. if the wire can carry a max current of 1.15 A how many turns of wire are neede to produce the desired B field?

 

[Nick89]

Can you try to find an expression for the magnetic field at the center of a solenoid?
(I think you cannot use Ampere's law here (since the length is only 13.3cm, if you use Ampere's law you assume the length is nearly infinite).)

The expression for B will be in terms of the current, the length, the radius, the permeability and the number of turns. Solve for the number of turns, and you can plug in your values.

 

[Nick89]

(I can't edit my post anymore..?)

Do you know Ampere's law?
Do you know Biot-Savart's law?
Do you know which one you must use here?

You could use Ampere's law, which makes the calculation lots easier, but it will also be much more of an approximation.
If you use Biot-Savart's law the magnetic field is more exact. I don't know how much the answer will vary depending on which method you use, it could well be that it is the same (since you will also have to round it to an integer, having 31.53 coils for example doesn't make sense..)