Determine inductance of a solenoid

[matt72lsu]

Homework Statement

Determine the inductance of a solenoid with 650 turns in a length of 21 cm. The circular cross section of the solenoid has a radius of 4.2 cm.

Homework Equations

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The Attempt at a Solution

I've looked all over my textbook and can't come up with a possible equation(s). Help!

 

[rl.bhat]

L = μo*N^2*A/l.
where N is number of turns,
A area of cross section of the coil and
l is the length of the coil.

 

[matt72lsu]

Ok so I did L = (1.26e-6)(650)^2(.00882) / .21 = 2.24e-2 H = 22.4mH. I got it wrong however. Where did I go wrong?

 

[rl.bhat]

Check the area of the coil.

 

[matt72lsu]

would area = .01764? (radius^2 (in meters) * .21)

 

[rl.bhat]

would area = .01764? (radius^2 (in meters) * .21)

Area of cross section of the coil is π*r^2.

 

[matt72lsu]

ok I'm an idiot. i got it wrong again. this was my equation: L = (1.26e-6)(650)^2(1.1466)/.21. i multiplied that answer by 1000 to get mH

 

[rl.bhat]

(1.1466)/
How did you get this?
Area = π*(4.2*10^-2)^2 m^2 = 55.42*10^-4 m^2

 

[matt72lsu]

ok i got it! i used n = 650 (is that not what n is?). Anyways... thanks for all your help (and patience). I really appreciate it!