# What do we mean with magnetic monopole and dipole?

1. What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes.

2. Also,what is their role in Gauss' law for magnetism (the net magnetic flux through a closed surface is zero)?

3. I read that the magnetic dipoles are essential for the meaning of this law. Why?

4. If magnetic monopoles existed,then why would the law not be valid?

5. Lastly,why do we say that the magnetic field is divergeless?

6. Some physicists try to find a magnetic monopole (something Dirac tried to explain i think). So if they actually find one, what does that mean?

7. For a classic magnet(N-S) we know that we have charges inside moving in a circular motion and they althogether form that magnetic field of the magnet. So how does finding a magnetic monopole change this? What does it mean for those small currents?

(I might understood something wrong here so enlighten me please!)

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes.

Luckily, there exists a truly amazing one-to-one correspondence between magnetism and electricity.

Monopole in magnetism is analogous to charge in electrostatics/electricity. Just like we have two types of charges (+ve & -ve), we have two types of monopoles (north & south). The north magnetic pole is also known as the positive pole and the south magnetic pole is known as the negative pole.

We refer to the size/magnitude of the charge as charge itself, but for a monopole, we refer to its size/magnitude as pole strength.

Electric charge is denoted by the letter 'q', the pole strength of a magnetic pole is denoted by the letter 'm'.

Electric charges produce electric fields. The magnetostatics analog is the magnetic field. We make use of electric field lines to represent the electric field visually. By convention, electric field lines start from a positive charge and terminate at a negative charge. So is the case with magnetic poles as well. Magnetic field lines originate from the north pole (+ve pole) and terminate at the south pole (-ve pole).

The strength of the magnetic field produced by a monopole is given by

$$\vec{B} = (\frac{\mu_o}{4\pi})\frac{m}{r^3}\vec{r}$$

You probably noticed that the equation is identical to Coulomb's law except for the fact that we have magnetic pole strengths instead of the magnitude of charge.

As of 2016, we aren't sure if magnetic monopoles exist (we haven't found one yet). When we try to make a monopole by slicing a bar magnet exactly in the middle, we end up creating two new bar magnets where each magnet has both north and south pole. Well, you might ask how do I know about the behavior of monopoles if monopoles don't exist. Whatever I said above is just a hypothesis and the hypothesis is consistent with the reality.

When two magnetic poles of equal pole strength are kept close to each other, we call it a dipole. A bar magnet is an example of a dipole. We have an electric dipole moment equivalent in magnetostatics. We call it magnetic dipole moment (usually represented by '$\vec{M}$').

$$M = md$$

where d is the distance between the two poles and m is the pole strength of the poles. The direction of the magnetic dipole momentum is from negative pole to the positive pole (In the case of an electric dipole, it is from the negative charge to the positive charge).

The field along the axis of the magnetic dipole is given by,

$$B = 2(\frac{\mu_o}{4\pi})\frac{M}{r^3}$$

and the field along the equatorial line of the dipole is given by

$$B = (\frac{\mu_o}{4\pi})\frac{M}{r^3}$$

If you open your textbook and look for the formulae of the electrostatics analogue of the dipole, you will find that the formulae are a perfect match.

The formulae given above can also be derived from the magnetic monopole hypothesis.

The similarities don't end here.

Torque on an electric dipole in an external uniform electric field is given by

$$\tau = \vec{p}\times\vec{E}$$

Torque on a magnetic dipole in an external uniform magnetic field is given by

$$\tau = \vec{M}\times\vec{B}$$

You shouldn't be surprised if you find more exact matches. The magnetic monopole behaves just like electric charge and the formulae are identical. The derivations for magnetic dipoles are identical to derivations for the electric dipoles so you should end up with the same formulae.

A circulating electric current behaves like a magnetic dipole. If you derive the formula for magnitude of magnetic field along the axis of the circular coil, you should get something similar to the following,

$$B = \frac{\mu_o NiR^2}{2(R^2 + x^2)^{\frac{3}{2}}}$$

where $N$ is the number of turns in the coil, $i$ is the current passing through the wire, $R$ is the radius of the coil and $x$ is the distance along the axis of the coil.

If we use the approximation $x>>R$, we get,

$$B = \frac{\mu_oNiR^2}{2x^3}$$

Rearranging further, we get

$$B = 2(\frac{\mu_o}{4\pi})\frac{(iN\pi R^2)}{x^3}$$

If you look carefully, you will notice that the formula looks very similar to the formula which gives the strength of the field along the axis of a magnetic dipole.

We can define magnetic dipole moment as

$$M = iN(\pi R^2)$$

The direction of the magnetic moment is the direction of the magnetic field at the center of the coil.

Now the formula looks pretty much identical to the formula given earlier for the strength of the field along the axis of a magnetic dipole.

In general, magnetic moment for any closed loop circuit can be defined as

$$\vec{M} = iN\vec{A}$$

where $\vec{A}$ is the unit normal vector for the loop.

1. Also,what is their role in Gauss' law for magnetism (the net magnetic flux through a closed surface is zero)?
2. I read that the magnetic dipoles are essential for the meaning of this law. Why?

3. If magnetic monopoles existed,then why would the law not be valid?

4. Lastly,why do we say that the magnetic field is divergeless?

One of the consequences of monopoles not existing is that magnetic field lines are always closed. Consider any dipole, a field line which emanates from the north pole must end up back at the south pole. The number of field lines that leave the surface is equal to the number of field lines entering the surface. Hence, there is no net flux entering or leaving the surface.

$$\oint{\vec{B}.d\vec{A}} = 0$$

In the Gauss Law for electrostatics, we consider the volume charge density or the net charge enclosed within the gaussian surface. The same goes for Gauss Law for magnetism.

$$\oint{\vec{B}.d\vec{A}} = \mu_o m_{enclosed}$$

since there can never be any isolated monopole, $m_{enclosed}$ is always zero.

If monopoles existed, then $m_{enclosed}$ needn't be zero. Hence, the Gauss law would be invalid.

Some physicists try to find a magnetic monopole (something Dirac tried to explain i think). So if they actually find one, what does that mean?

If we ever find a monopole, it would imply that Gauss law for magnetism would be invalid. We will need to amend the law to make allowance for monopoles. (the amended version of the law was presented in the answer to your previous question)

Discovery of magnetic monopoles would imply the existence of magnetic currents. We would have a new chapter in our physics textbooks. Possibly a new engineering branch might appear (magnetronics?).

For a classic magnet(N-S) we know that we have charges inside moving in a circular motion and they althogether form that magnetic field of the magnet. So how does finding a magnetic monopole change this? What does it mean for those small currents?

Every electron has two types of magnetic dipole moment, namely spin magnetic dipole moment and orbital magnetic dipole moment.

There are several electrons in an atom and most electrons cancel out each other's magnetic moment. When all the electrons cancel out neatly, the total magnetic moment of the atom is zero. The substances where the total magnetic moment of the constituent atoms is zero are known as diamagnetic substances.

There are many substances with unpaired electrons. This gives rise to a net magnetic moment for each atom. When these atoms collectively align in the same direction. This kind of collection of atoms is known as a domain. When domains align to give a net magnetic moment to a substance, the substance is said to be ferromagnetic.

Discovery of a magnetic monopole shouldn't affect the existing theories. However, it might force us to investigate further at the fundamental level.

Monopoles: Either north or south pole alone. Dipoles: Both north and south pole in each other's influence

The Magnetic field of lines originate from North Pole and end at south pole. Gauss's law of Magnetostatics states that total magnetic flux from a closed surface is zero. That is number of incoming field line equals the number of outgoing lines. I.E. there should be both poles of equal magnitude present inside the surface. If monopoles existed then only the field lines would be going outside or coming inside at once, which will clearly violate Gauss law.

• How can there be a magnetic monopole?Because a current produces a dipole.Like in a magnet,there are very small particles moving in circles producing that magnetic field.What changes for the "current produces magnetic field"? – TheQuantumMan Apr 2 '15 at 18:06
• @LandosAdam There can't be as I am telling by Gauss's theorem. – Kishan Kumar Apr 2 '15 at 18:10
• The magnetic field in a magnet does not "originate at the north pole and end at the south pole". In fact it forms closed loops, the field doesn't end at the south pole, it continues along inside the magnet until it reaches the north pole again, forming a closed loop. Which is rather the point; magnetic field lines don't start or end anywhere, they always form closed loops. – Peter Webb Apr 2 '15 at 18:10
• Let me edit my question in a moment – TheQuantumMan Apr 2 '15 at 18:11
• Yes sorry for that mistake. They form closed continuous loop unlikes electric fields. – Kishan Kumar Apr 2 '15 at 18:12

The magnetic field in a magnet does not "originate at the north pole and end at the south pole". In fact it forms closed loops, the field doesn't end at the south pole, it continues along inside the magnet until it reaches the north pole again, forming a closed loop. Which is rather the point; magnetic field lines don't start or end anywhere, they always form closed loops.