Length of wire wrapped around a solenoid?

In summary, the problem asks for the length of super conducting cable needed to wind a solenoid with a diameter of 3m, length of 5m, and 1164 turns. Using the formula for circumference, (2pi * radius), the length of one loop of wire is found to be 6πm. Multiplying this by 1164, the total length of wire needed is approximately 6,958.769m.
  • #1
kylesss
1
0

Homework Statement


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?"

Homework Equations


Circumference = 2pi*radius

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!
 
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  • #2
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
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
Welcome to PF;
Kneeproblems said:
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)
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:
  • #5
kylesss said:

Homework Statement


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?"


Homework Equations


Circumference = 2pi*radius


The Attempt at a Solution


My approach was: Multiply (2pi * 1.5m) * (1164 turns) * (5m) = 54852m
Check again why you include the part in red? 2Pi * 1.5m is the distance all the way around the cylinder, just once.
 
  • #6
Simon Bridge said:
Nice attempt - and it's what I thought of at first: but it gives the wrong answer!
Wrong? How do you know what answer the textbook is expecting? :wink:

If we consider each turn to be on a slight slant, my calculation of length remains the same (expressed to 6 sig figs).
 
  • #7
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
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 = ?
 

Related to Length of wire wrapped around a solenoid?

1. What is a solenoid?

A solenoid is a coil of wire that creates a magnetic field when an electric current passes through it. It is commonly used in electronic devices such as electromagnets, transformers, and speakers.

2. How does the length of wire wrapped around a solenoid affect its magnetic field?

The length of wire wrapped around a solenoid directly affects the strength of its magnetic field. The longer the wire, the stronger the magnetic field. This is because a longer wire creates more loops in the coil, resulting in a stronger magnetic field.

3. What is the relationship between the number of turns and the length of wire in a solenoid?

The number of turns in a solenoid is directly proportional to the length of wire. This means that as the number of turns increases, the length of wire also increases. This relationship is important because it determines the strength of the magnetic field produced by the solenoid.

4. How does the material of the wire affect the length of wire wrapped around a solenoid?

The material of the wire does not directly affect the length of wire wrapped around a solenoid. However, the type of wire used can impact the efficiency and strength of the solenoid's magnetic field. Thicker wires with low resistance are generally better for creating strong magnetic fields.

5. How can the length of wire wrapped around a solenoid be calculated?

The length of wire wrapped around a solenoid can be calculated using the formula: L = N x C, where L is the length of wire, N is the number of turns, and C is the circumference of the solenoid. The circumference can be calculated by multiplying the diameter of the solenoid by pi (π).

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