# How Many Turns of Wire Does the Coil Have?

• feedmeister
In summary: A m^2 is placed on the negative x-axis, with a compass located at the origin in the negative z direction. Between the magnet and the compass is a coil of wire with a radius of 1.5 cm. The distance between the coil and compass is 9.2 cm and the distance between the magnet and compass is 22.5 cm. A steady current of 0.632 amperes flows through the coil in a clockwise direction when viewed from the compass. The equation for calculating the magnetic field of the loop is given, as well as the equations for the magnetic field of the magnet and the Earth. The number of turns
feedmeister

## Homework Statement

A bar magnet with magnetic dipole moment 0.51 A m^2 lies on the negative x-axis, as shown in the diagram. A compass is located at the origin. Magnetic North is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 1.5 cm, connected to batteries not shown in the picture. The distance from the center of the coil to the center of the compass is 9.2 cm. The distance from the center of the bar magnet to the center of the compass is 22.5 cm. A steady current of 0.632 amperes runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass.

How many turns of wire are in the coil?

## Homework Equations

$$B_{loop} = \mu_{0}2\pi R^{2}I/{4\pi}(z^{2}+R^{2})^{3/2}$$
$$B_{magnet} = \mu_{0}2\mu/4\pi r^{3}$$
$$B_{earth}$$= 2 E-5 Tesla

$$\mu_{0}/4\pi = 10^{-7}$$
I = 0.632 A
$$\mu = 0.51 A m^{2}$$

## The Attempt at a Solution

I have been trying to do # of turns = $$(B_{earth} - B_{magnet}) / B_{coil}$$
and got 100.1271 but it's not the right answer. Can anyone help with what I'm doing wrong?

Attached is a diagram of the problem.

Thanks and regards,

#### Attachments

• coil_magnet_compass_2a.gif
10.6 KB · Views: 855
Yeah I figured it out. It's actually just Bmagnet/Bcoil.

Thanks,

Hello ,

Thank you for sharing your attempt at solving this problem. It seems like you have a good understanding of the equations and concepts involved in finding the number of turns in a coil. However, there are a few things that may have led to an incorrect answer.

Firstly, I would recommend double-checking your units. In the equation for B_{loop}, the units for R and z should be in meters, while the units for I should be in amperes. Additionally, the units for B_{magnet} and B_{earth} should be in tesla, not amperes per meter. Making sure all units are consistent and in the correct form can help avoid errors in calculations.

Secondly, it may be helpful to break down the problem into smaller steps. For example, you could first calculate the magnetic field from the loop of wire at the location of the compass, using the given dimensions and current. Then, you could calculate the magnetic field from the bar magnet at the same location. Finally, you can subtract these two values to find the total magnetic field at the location of the compass. This total magnetic field can then be used in your equation to find the number of turns in the coil.

I hope this helps guide you towards the correct solution. Keep up the good work!

Best,

## 1. How does the number of turns of wire in a coil affect its performance?

The number of turns of wire in a coil, also known as the coil's winding density, directly affects its inductance and resistance. A higher number of turns results in a higher inductance and higher resistance, which can improve the coil's performance in applications such as transformers and electromagnets.

## 2. What is the relationship between the diameter of the wire and the number of turns in a coil?

The diameter of the wire and the number of turns in a coil have an inverse relationship. This means that as the wire diameter increases, the number of turns decreases, and vice versa. This relationship is important to consider when designing a coil for a specific application, as it can affect the coil's overall performance.

## 3. Can the number of turns in a coil be changed after it has been wound?

It is possible to change the number of turns in a coil after it has been wound, but it can be challenging and may require special equipment. If the coil is already in use, it is generally not recommended to change the number of turns as it can significantly affect the coil's performance.

## 4. How does the material of the wire affect the number of turns in a coil?

The material of the wire used in a coil can affect the number of turns needed to achieve a desired inductance. For example, a coil made with copper wire will require fewer turns than a coil made with steel wire to achieve the same inductance. This is because copper has a higher conductivity, allowing for a stronger magnetic field with fewer turns.

## 5. What is the purpose of varying the number of turns in a coil?

Varying the number of turns in a coil allows for customization of the coil's inductance, resistance, and other properties. This can be beneficial in applications where specific values are needed, such as in electronic circuits or electric motors. It also allows for optimization of the coil's performance in different environments or for different purposes.

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