# Magnetic Field Problem (Wire within a Tube)

• loto
In summary, the conversation is about a cylindrical tube carrying a current and a wire running along its axis carrying an opposite current. The question is about the magnetic field created by these currents, with options for the field being zero or non-zero in different areas. After considering Ampere's Law and the concept of cylindrical symmetry, it is concluded that the field will be zero inside the tube and non-zero elsewhere. This is because the enclosed currents will cancel out when the radius of the Amperian loop is greater than the outer radius of the tube. The conversation ends with the understanding that the field will only be present outside the tube and the person expressing gratitude for the explanation.
loto
Well, I was going through some example problems to study for a test and came upon one I can't figure out. Here is the question:

A long straight cylindrical tube has an inner radio Ri and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire which runs along the tube axis carries a current of the same magnitude but opposite in direction.

The magnetic field created by these currents is:
A. zero outside the tube, but non-zero elsewhere
B. zero inside the tube, but non-zero elsewhere
C. zero everywhere
D. zero outside the tube and in the conducting material of the tube, but nonzero inside the tube
E. non-zero everywhere

I really should know this, but seem to be having a brain fart. Since the currents are opposite, the magnetic fields will be opposite in direction but equal in magnitude. Now, I would think this would mean that the field would be zero inside the tube and non-zero elsewhere, but something seems wrong with that.

Any hints would be greatly appreciated!

Consider Ampere's Law. This arrangement has cylindrical symmetry, so the field at any radius from the center can be easily related to the total current passing through a circle with that radius.

Ahh, I understand. If the radius of the Amperian loop is less than the outer radius of the tube, the enclosed current will not equal zero. However, as soon as the radius of the loop is greater than that of the outer edge of the tube the two equal enclosed currents will negate each other and there will be no field.

At least, I think I understand. Thank you very much.

Sounds like you've got it.

## 1. What is a magnetic field problem?

A magnetic field problem refers to the study and analysis of the behavior and interaction of magnetic fields within a given space, typically involving a wire within a tube. This can involve calculations and observations of the strength, direction, and effects of the magnetic field.

## 2. How is a magnetic field problem solved?

A magnetic field problem can be solved using mathematical equations, such as Ampere's Law or the Biot-Savart Law, to calculate the magnetic field strength and direction at a given point. It also involves understanding the properties of the materials involved, such as the permeability of the tube and the current flowing through the wire.

## 3. What factors affect a magnetic field problem?

Several factors can affect a magnetic field problem, including the strength and direction of the current flowing through the wire, the distance between the wire and the tube, and the properties of the materials involved. Other factors may include the shape and orientation of the wire and the tube, as well as any external magnetic fields present.

## 4. What are some real-world applications of magnetic field problems?

Magnetic field problems have many practical applications, such as in electromagnets used in machinery and equipment, magnetic levitation systems in transportation, and medical imaging technologies, such as MRI machines. They are also essential in understanding and predicting the behavior of Earth's magnetic field and its impact on navigation and communication systems.

## 5. How can understanding magnetic field problems benefit society?

Understanding magnetic field problems allows for the development and improvement of various technologies that have a significant impact on society. This includes advancements in transportation, healthcare, and communication systems, as well as the ability to study and better understand natural phenomena, such as the Earth's magnetic field and its effects on the environment and living organisms.

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