# Length of wire wrapped around a solenoid?

1. Mar 9, 2014

### kylesss

1. The problem statement, all variables and given/known data
Hi everyone, the problem I'm stuck on reads: " Imagine a solenoid 3m in diameter, 5m long having 1164 turns of super conducting cable. What length of super conducting cable is used to wind this solenoid?"

2. Relevant equations
Circumference = 2pi*radius

3. The attempt at a solution
My approach was: Multiply (2pi * 1.5m) * (1164 turns) * (5m) = 54852m

I would greatly appreciate help :) Thank you for your time!

2. Mar 9, 2014

### Simon Bridge

Welcome to PF;
The solenoid has N turns of diameter D along length L. You want to find the length x of the wire in those turns.

Right away you can see that: $L > \pi DN$ because the wire must go diagonally around the cylinder - or, at least, do a little dogleg every turn.

The wire going diagonally should be a hint: how do you find the length of something that goes diagonally if you know the height and the base?

If the cylinder had only one turn going around it - how long would the wire be?
Try again for 2 turns ... spot the pattern?

3. Mar 10, 2014

### Kneeproblems

Watch your units. You are looking for length of wire, and the answer you got is area.

Try looking at it as an individual segment. What is the length of one loop of wire? C = pi * d

What is the length of 1164 loops of wire? (multiply C by # or loops)

4. Mar 10, 2014

### Simon Bridge

Welcome to PF;
Nice attempt - and it's what I thought of at first: but it gives the wrong answer!

Consider: If the cylinder had only one loop of wire around it - how long is the wire?
Hint: the wire goes in a spiral.

---------------------------------

Aside: typo in post #2: $L=\pi DN$ should be $x > \pi DN$

Last edited: Mar 10, 2014
5. Mar 11, 2014

### Staff: Mentor

Check again why you include the part in red? 2Pi * 1.5m is the distance all the way around the cylinder, just once.

6. Mar 11, 2014

### Staff: Mentor

Wrong? How do you know what answer the textbook is expecting?

If we consider each turn to be on a slight slant, my calculation of length remains the same (expressed to 6 sig figs).

7. Mar 11, 2014

### Simon Bridge

Good point - it is a lot of turns.
A book probably only expects 2sig fig at most.
However - that makes the inclusion of the length of the solenoid as superfluous ... it would be interesting to see if that's a deliberate red herring (hoping student would realize the approximation would be good enough) or a trap for a long-answer problem which is awarded marks.

8. Mar 11, 2014

### rude man

Seems to me the length of the solenoid is immaterial. The wire diameter is not given so pick it any size you want.
1164 x coil diameter = ?

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