# Why would a magnetic monopol's field be 1/r^2?

• Yonah
In summary, the conversation discusses the concept of magnetic monopoles and their behavior in relation to electric charges. The possibility of their existence is based on the idea of symmetry in Maxwell's equations. However, the equations would not be symmetrical if magnetic monopoles did not behave like electric monopoles. The conversation also addresses the potential implications on Maxwell's equations if magnetic monopoles followed a different pattern of decrease than 1/r^2. Ultimately, the focus is on achieving symmetry in the equations.
Yonah
Hi,
I was reading Purcell's Electricity and Magnetism. It says that if there were a magnetic charge, its field would behave like an electric charge (field pointing out radially and magnitude decreasing as 1/r^2). Why? Could this be deduced from magnetic fields produced by electric charges? If so, how?

The only reason to think that magnetic monopoles exist is because it would make things like Maxwells equations more symmetrical. If they didn't behave like an electric monopole then that would make the equations asymmetrical, which would defeat the whole point.

Ok, so you are saying that there would be no contradiction among maxwell's equations necesarily (except of course ∇⋅B=0) if a magnetic monopol existed which decreased in a way other than 1/r^2. Things just wouldn't be symetrical in that case. Is that correct?

If the ##\vec B## field from a magnetic monopole did not go like ##1/r^2##, what would replace ##\vec \nabla \cdot \vec B = 0## and its integral equivalent ##\oint {\vec B \cdot d \vec a } = 0##?

Yonah said:
Ok, so you are saying that there would be no contradiction among maxwell's equations necesarily (except of course ∇⋅B=0) if a magnetic monopol existed which decreased in a way other than 1/r^2. Things just wouldn't be symetrical in that case. Is that correct?
No, that isn't what I am saying. I am saying that to my knowledge nobody even considers that. The idea is to make Maxwell's equations more symmetrical, not less. I don't know how a change like the one you describe could wind up with a set of equations even remotely similar to Maxwells equations. It would be the complete opposite of what monopole proponents want to accomplish.

Ok, I think I understand what your getting at. Thanks!

## 1. Why is the magnetic field of a magnetic monopole inversely proportional to the square of the distance from the monopole?

The inverse square law is a fundamental law of physics that applies to many natural phenomena, including the magnetic field of a magnetic monopole. This law states that the strength of a field decreases with the square of the distance from its source. Therefore, as the distance from a magnetic monopole increases, the magnetic field strength decreases exponentially.

## 2. Is the 1/r^2 relationship for the magnetic field of a magnetic monopole the same as that of a point charge?

Yes, the 1/r^2 relationship for the magnetic field of a magnetic monopole is analogous to the 1/r^2 relationship for the electric field of a point charge. This is because both magnetic monopoles and point charges are considered to be fundamental sources of their respective fields, and both obey the inverse square law.

## 3. How is the strength of a magnetic monopole's field affected by the distance from the monopole?

As mentioned before, the strength of a magnetic monopole's field is inversely proportional to the square of the distance from the monopole. This means that as the distance increases, the strength of the field decreases exponentially. Conversely, as the distance decreases, the field strength increases exponentially.

## 4. Can the strength of a magnetic monopole's field be accurately measured at any distance?

Yes, the strength of a magnetic monopole's field can be measured at any distance using specialized equipment such as a magnetometer. However, as the distance from the monopole increases, the field strength becomes weaker and may be more difficult to measure accurately.

## 5. Does the 1/r^2 relationship for the magnetic field of a magnetic monopole hold true for all distances?

No, the 1/r^2 relationship for the magnetic field of a magnetic monopole is only valid for distances that are much larger than the size of the monopole itself. At very close distances, the field behavior may deviate from the inverse square law due to the effects of the monopole's finite size and shape. However, for most practical applications, the 1/r^2 relationship can be considered accurate.

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