Inductance Of A Solenoid Problem

[pierretong]

Homework Statement

A solenoid is wound with a single layer of insulated copper wire of diameter 2.100 mm and has a diameter of 3.000 cm and is 1.900 m long. Assume that adjacent wires touch and that insulation thickness is negligible.

a) How many turns are on the solenoid?
Solved: determined to be 904

b)What is the inductance per meter (H/m) for the solenoid near its center?

Homework Equations

Inductance = (constant mu0)* (N^2)*A / l

mu0 = 4*PI*10^-7
N = 904 turns
A = PI*R^2 (R = 2.100 mm/2)
l = length of solenoid = 1.900 m

The Attempt at a Solution

Plugged all those variables above (converted R to meters) and got 0.00019 for the inductance.

I don't understand what it means to find the Inductance per Meter at the center of the solenoid? Do I have to divide by 1.900 m again? Confused as to what I'm supposed to do.

 

[tiny-tim]

hi pierretong!

I don't understand what it means to find the Inductance per Meter at the center of the solenoid? Do I have to divide by 1.900 m again?

yes, your formula µN²A/l gives the inductance of the whole solenoid

so divide by l again for the inductance per metre

(if you cut the solenoid into x pieces, then for one piece N² would be 1/x², so N²/l would be 1/x)

see also http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indcur.html#c2 and http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indsol.html

 

[gneill]

Homework Statement

A solenoid is wound with a single layer of insulated copper wire of diameter 2.100 mm and has a diameter of 3.000 cm and is 1.900 m long. Assume that adjacent wires touch and that insulation thickness is negligible.

a) How many turns are on the solenoid?
Solved: determined to be 904

b)What is the inductance per meter (H/m) for the solenoid near its center?

Homework Equations

Inductance = (constant mu0)* (N^2)*A / l

mu0 = 4*PI*10^-7
N = 904 turns
A = PI*R^2 (R = 2.100 mm/2)
l = length of solenoid = 1.900 m

The Attempt at a Solution

Plugged all those variables above (converted R to meters) and got 0.00019 for the inductance.

I don't understand what it means to find the Inductance per Meter at the center of the solenoid? Do I have to divide by 1.900 m again? Confused as to what I'm supposed to do.

Check the area calculation. You want the cross sectional area of the solenoid, so which radius should you use?