# Magnetic field far from the origin

In summary, an important result in the theory of antennas states that if a current passes through the ZZ axis, the magnetic field at a far distance can be expressed in spherical coordinates using only one component of the magnetic vector potential. To prove this, we can use the equations for the magnetic field of a straight wire and B=∇xA. This concept relates to the radiated EM wave, which falls off inversely with distance and has a maximum at 90 degrees to the conductor.

## Homework Statement

An important result in the theory of antennas, is that if a current passes through the ZZ axis, the magnetic field far from the origin can be expressed in spherical coordinates, using only one componente of the magnetic vector potential.
Prove that:

## Homework Equations

The magnectic field for a straight wire is mu0*I/(2*pi*r), and B=∇xA.

## The Attempt at a Solution

This was in my exam last week, and i have no idea how to solve it... I've tried stating with the magnetic field of a straight wire, but i don't know how to relate that with the curl of A. Can you guys please help me out?

## Homework Statement

An important result in the theory of antennas, is that if a current passes through the ZZ axis, the magnetic field far from the origin can be expressed in spherical coordinates, using only one componente of the magnetic vector potential.
Prove that:

## Homework Equations

The magnectic field for a straight wire is mu0*I/(2*pi*r), and B=∇xA.

## The Attempt at a Solution

This was in my exam last week, and i have no idea how to solve it... I've tried stating with the magnetic field of a straight wire, but i don't know how to relate that with the curl of A. Can you guys please help me out?

## Homework Statement

An important result in the theory of antennas, is that if a current passes through the ZZ axis, the magnetic field far from the origin can be expressed in spherical coordinates, using only one componente of the magnetic vector potential.
Prove that:

## Homework Equations

The magnectic field for a straight wire is mu0*I/(2*pi*r), and B=∇xA.

## The Attempt at a Solution

This was in my exam last week, and i have no idea how to solve it... I've tried stating with the magnetic field of a straight wire, but i don't know how to relate that with the curl of A. Can you guys please help me out?
Well I think at a great distance, we are talking about the magnetic field of the radiated EM wave. These fields, when radiated from a short conductor, will fall off inversely with distance, have a maximum at 90 degrees to the conductor and a radiation pattern which falls off with the cosine of this angle. Maybe this description will help?

## 1. What is a magnetic field?

A magnetic field is a physical phenomenon that is created by electric currents and results in the force of attraction or repulsion between magnetic materials.

## 2. How does the magnetic field change as distance from the origin increases?

The strength of a magnetic field decreases as distance from the origin increases. This is due to the inverse square law, which states that the strength of a field is inversely proportional to the square of the distance from the source.

## 3. Can a magnetic field exist infinitely far from the origin?

In theory, a magnetic field can extend infinitely far from the origin. However, in reality, the strength of the field decreases to the point where it becomes undetectable at a certain distance.

## 4. What factors affect the strength of a magnetic field far from the origin?

The strength of a magnetic field far from the origin is affected by the strength of the source, the distance from the source, and any intervening materials that may alter the field.

## 5. How is the direction of a magnetic field determined far from the origin?

The direction of a magnetic field at any point is determined by the direction of the magnetic force that would be experienced by a hypothetical test magnet placed at that point.

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