# Calculate Magnetic Induction in Cylindrical Hole w/ Uniform Current

• Crazy Gnome
In summary, the conversation discusses calculating the magnetic induction B inside an infinite cylindrical hole parallel to a wire with a uniform current density. The individual is confused about the result being 0 according to Ampere's law and doubts this answer because they are asked to plot B as a function of radius. They are then given a hint to solve the problem by imagining how the hole can be produced using two cylinders.
Crazy Gnome
Question: An infinite cylindrical wire with radius 2R caries a uniform current density J=Jz, except in an infinite cylindrical hole parallel to the wires axis. The hole has a radius of R and is tangent to the exterior of the wire. Calculate the magnetic induction B everywhere inside the hole.

It would seem to me that according to Ampere's law B inside the cavity would just be 0 because there is no enclosed current. What am I missing? And the reason I doubt my answer so much is that he then wants us to plot B as a function of radius in the hole and I can't imagine plotting 0 was his intention.

Crazy Gnome said:
Question: An infinite cylindrical wire with radius 2R caries a uniform current density J=Jz, except in an infinite cylindrical hole parallel to the wires axis. The hole has a radius of R and is tangent to the exterior of the wire. Calculate the magnetic induction B everywhere inside the hole.

It would seem to me that according to Ampere's law B inside the cavity would just be 0 because there is no enclosed current. What am I missing? And the reason I doubt my answer so much is that he then wants us to plot B as a function of radius in the hole and I can't imagine plotting 0 was his intention.

Here's a hint to solving the problem: imagine how you can produce that hole by superposing two cylinders.

## 1. What is magnetic induction?

Magnetic induction, also known as magnetic flux density, is a measure of the strength of a magnetic field. It is typically denoted by the symbol B and is measured in units of tesla (T) or gauss (G).

## 2. What is a cylindrical hole with uniform current?

A cylindrical hole with uniform current refers to a situation where a cylindrical conductor has a steady flow of electrical current passing through it. The current is evenly distributed throughout the conductor and does not change with time.

## 3. How is magnetic induction calculated in a cylindrical hole with uniform current?

The formula for calculating magnetic induction in a cylindrical hole with uniform current is B = μ0I/2πr, where B is the magnetic induction, μ0 is the permeability of free space, I is the current, and r is the distance from the center of the hole to the point where the magnetic induction is being calculated.

## 4. What is the significance of calculating magnetic induction in a cylindrical hole with uniform current?

Calculating magnetic induction in a cylindrical hole with uniform current is important in understanding and predicting the behavior of magnetic fields. It is also useful in the design and analysis of devices that utilize magnetic fields, such as electric motors and generators.

## 5. Are there any practical applications of calculating magnetic induction in a cylindrical hole with uniform current?

Yes, there are several practical applications of calculating magnetic induction in a cylindrical hole with uniform current. Some examples include the design and optimization of magnetic sensors, the development of magnetic levitation systems, and the analysis of magnetic fields in medical imaging devices.

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