# Calculting the length of a solenoid

• Taylor_1989
In summary, the magnetic field in the center of a one-turn circular coil is H=0.0016 N/m. In the second instance, when the wire was wound 500 times to form the solenoid, the magnetic field is H and B inside the solenoid, far from the edges.
Taylor_1989

## Homework Statement

Q2

A Cu wire of circular section and diameter 0.2 mm is used to form a one-turn coil and also to form a solenoid. Both have a radius of 2 cm. In both cases, a 10 mA current flows through the wire.

a)Work out the magnetic field H in the centre of the one-turn circular coil.
b) In the second instance, when the wire was wound 500 times to form the solenoid, work out the magnetic field H and B inside the solenoid, far from the edges.

## The Attempt at a Solution

So I am having a issue with my ans to the mark scheme ans for this question, so my first correct, but when I go to calculate the second part this is where thing go a miss.

The equation I am using for magnetic field intensity is
$$H=\frac{I \cdot N}{L}$$
Now from the question I think L is the length of the conductor, which I believe to be 4cm 2 time the diameter.

But when I got to check my answer, it states that
$$L=N*r=500*0.2mm$$
which is the diameter of the wire, but how is this the length of the solenoid, could someone please explain, or have I miss understood the question or worse the physics?

Taylor_1989 said:
Now from the question I think L is the length of the conductor, which I believe to be 4cm 2 time the diameter.
For the field within a solenoid, L is the length of the solenoid. (What matters is the number of turns per length: N/L.)

I am not sure what you mean by number of turns per length, 1000/0.04, how dose this related to the diameter that thye have given, has I can't see how the diameter is playing a role in this.

Taylor_1989 said:
I am not sure what you mean by number of turns per length, 1000/0.04, how dose this related to the diameter that thye have given, has I can't see how the diameter is playing a role in this.
Assume that the solenoid is just one layer thick. So the diameter of the wire, and the number of turns, tells you the length of the solenoid.

But is the question not saying that I have a long peace of wire, I then form a circular loop with that wire, which has a radius of 2cm so the actual wire length is 4cm. I mean could then get that same 4cm wire and form 1000 loop with it it still 4cm? This is how I am seeing the question.

No, treat these as two separate problems. You have a spool of wire and you make a single loop with the given radius. The length of the wire is 2*pi*r, of course.

For the solenoid you'll be making 500 loops, so you'll need more wire. (500 times more!)

AH! okay, thank you, now it make sense, I kept thinking I have a wire of 4cm and that was it, I did think it was strange that it was saying 500 turns but I ignored (which I shouldn’t of).

Once again thank you, I will try to read the question more carefully next time.

Good!

## 1. How do you calculate the length of a solenoid?

The length of a solenoid can be calculated using the formula L = (μ0 * N^2 * A) / (2 * μr * l), where L is the length, μ0 is the permeability of free space, N is the number of turns, A is the cross-sectional area, μr is the relative permeability, and l is the length of the solenoid.

## 2. What is the significance of calculating the length of a solenoid?

Calculating the length of a solenoid is important for determining its properties, such as its inductance and magnetic field strength. It also allows for the design and optimization of solenoids for various applications, such as in electronic devices and electromagnets.

## 3. How does the number of turns affect the length of a solenoid?

The number of turns in a solenoid is directly proportional to its length. This means that as the number of turns increases, the length of the solenoid also increases. This relationship is described by the formula L ∝ N^2, where L is the length and N is the number of turns.

## 4. Can the length of a solenoid be adjusted?

Yes, the length of a solenoid can be adjusted by changing the number of turns, the cross-sectional area, or the length of the solenoid itself. These changes will affect the magnetic field strength and inductance of the solenoid.

## 5. How accurate is the calculation of the length of a solenoid?

The calculation of the length of a solenoid is based on idealized assumptions and may not always be completely accurate. Factors such as the shape and material of the solenoid may affect the actual length. However, the formula provides a good estimate and is commonly used in practice.

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