# What is the magnetic field of a half toroid?

• Engineering
• VelocityOfTheSound
In summary, the conversation discusses the magnetic field of a half toroid and the methods for calculating it. One method suggested is using Ampere's law, while the other is using Biot-Savart's law. There is also mention of possible mistakes and the complexity of the problem.
VelocityOfTheSound
Homework Statement
What is the magnetic field of a half toroid?
Relevant Equations
Magnetic field of a toroid: μo*N*i / 2*pi*r
Hello,
I would like to know what is the magnetic field of a half toroid.

Would we use Ampere's law? So, considering that the integral is equal to BA, we would have BA = μo * i, then B = (μo * i) / r. But, using Biot-Savart's law, by symmetry, it seems that the vector sum of all the differential magnetic fields is zero.

What is the true answer for this problem? How can I find it? Where are my mistakes?

Thank you!

Just to be certain: cut in half which way? Air core? This is likely not simple.

hutchphd said:
Just to be certain: cut in half which way? Air core? This is likely not simple.
I will show an image.

#### Attachments

• Half-toroid.jpg
6.7 KB · Views: 133

## 1. What is a half toroid?

A half toroid is a three-dimensional shape that resembles a half of a donut or a tire. It is formed by rotating a semi-circle around a central axis.

## 2. What is the purpose of a half toroid?

A half toroid is commonly used in electromagnetism and electronics to create a magnetic field. It is also used in mechanical systems as a way to transmit rotational motion.

## 3. How is the magnetic field of a half toroid created?

The magnetic field of a half toroid is created by passing an electric current through a wire that is wrapped around the toroid's curved surface. The direction of the magnetic field depends on the direction of the current flow.

## 4. What factors affect the strength of the magnetic field in a half toroid?

The strength of the magnetic field in a half toroid is affected by the number of turns in the wire, the amount of current flowing through the wire, and the radius of the toroid's curved surface. The material of the toroid also plays a role in the strength of the magnetic field.

## 5. How is the magnetic field of a half toroid measured?

The magnetic field of a half toroid can be measured using a magnetic field sensor, such as a magnetometer. The sensor is placed at various points around the toroid's surface, and the strength of the magnetic field is recorded. The measurements can then be used to map out the shape and strength of the magnetic field.

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