# Understanding Magnetic Induction Field B on Circular Coil Axis

• retupmoc
In summary, the conversation is about finding the magnetic induction field B on the axis of a circular coil. The field must be along the x-axis and it is denoted as (dlxr )x. The angle between dl and r is denoted as alpha, but there is confusion about whether x and alpha are the same angle. The integrand is along every dl, while the radius A rides along its resident circle once. It is mentioned that the Biot-Savart-Laplace law should be used, as Laplace created the formula and other scientists worked with magnets. The same can be said for the Stefan-Boltzmann law, where Boltzmann was the theorist and Stefan was the experimentalist.
retupmoc
Just a quick question about finding the magnetic induction field B on the axis of a circular coil shown on page 7 on http://www.physics.gla.ac.uk/~dland/ELMAG305/Elmag305txt5.pdf
I understand why the field must be along the x-axis but why does (dlxr )x become dlrsin(alpha)? alpha doesn't seem to be the angle between the dl and r, dlxr would equal |dl|| r |sin(x) where x would be the angle between the dl and r. My problem is x and alpha don't seem to be the same angle so i don't know how to advance with this problem. Any help?

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You can't denote the angle with "x",one of the axis with "Ox" and the sign for a vector/cross product with "x"...Let the angle be "alpha",the axis "Ox" and the sign $$\times$$.

Daniel.

I don't see why alpha wouldn't be that angle. What angle are you suggesting?

A is the radius of the circle, and r is the line drawn from the center of the loop at a distance x_i away. You are integrating I along every dl, during which the radius A rides along its resident circle once.

Oh,and it should be Biot-Savart-Laplace law...Laplace was the mathematician who made the formula up,while the other guys fooled around with magnets.

The same story with Stefan-Boltzmann law...Boltzmann was the theorist,and Stefan the experimentalist.

Daniel.

## 1. What is magnetic induction field B on a circular coil axis?

The magnetic induction field B on a circular coil axis is a measure of the strength and direction of the magnetic field produced by an electric current passing through a circular coil. It is a vector quantity, meaning it has both magnitude and direction, and is typically measured in units of tesla (T) or gauss (G).

## 2. How is magnetic induction field B on a circular coil axis calculated?

The magnetic induction field B on a circular coil axis is calculated using the following formula: B = μ₀NlI / R, where μ₀ is the permeability of free space, N is the number of turns in the coil, l is the length of the coil, I is the current passing through the coil, and R is the radius of the coil. This formula is also known as Ampere's law.

## 3. What factors affect the strength of the magnetic induction field B on a circular coil axis?

The strength of the magnetic induction field B on a circular coil axis is affected by several factors, including the strength of the current passing through the coil, the number of turns in the coil, the length of the coil, and the radius of the coil. Additionally, the magnetic permeability of the material inside the coil can also affect the strength of the magnetic field.

## 4. How does the direction of the magnetic induction field B on a circular coil axis relate to the direction of the current passing through the coil?

The direction of the magnetic induction field B on a circular coil axis is perpendicular to the direction of the current passing through the coil. This means that if the current is flowing clockwise through the coil, the magnetic field will be directed out of the coil in a counterclockwise direction.

## 5. What are the practical applications of understanding magnetic induction field B on a circular coil axis?

Understanding magnetic induction field B on a circular coil axis is important in a variety of scientific and technological fields. It is particularly useful in the design of electrical devices such as motors, generators, and transformers. It is also used in medical imaging techniques like magnetic resonance imaging (MRI), as well as in the study of Earth's magnetic field and other celestial bodies.

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