Magnetism & Matter: Q&A on Electrons & Fields

[Prannoy Mehta]

Q1.In school, we were learning about the magnetic properties of solids, and my teacher mentioned this, a spinning electrons create magnetic field. I cannot understand how. Like earlier we were told if a charge is in motion, it creates magnetic field, but in spinning, it does not have translation. It's in one place. I would like to add this as a question, a wire of current I is moving in +y axis and a electron is revolving at a distance of x m along +k direction, does it feel any magnetic force, and what if it was spinning along +y direction.

Q2.Why are magnets always in dipoles, and further, why magnetic fields form closed loops, while electric fields are open loops.

Thanks in advance for clearing the doubts.

 

[sunmaggot]

Q1.In school, we were learning about the magnetic properties of solids, and my teacher mentioned this, a spinning electrons create magnetic field. I cannot understand how. Like earlier we were told if a charge is in motion, it creates magnetic field, but in spinning, it does not have translation. It's in one place. I would like to add this as a question, a wire of current I is moving in +y axis and a electron is revolving at a distance of x m along +k direction, does it feel any magnetic force, and what if it was spinning along +y direction.

Q2.Why are magnets always in dipoles, and further, why magnetic fields form closed loops, while electric fields are open loops.

Thanks in advance for clearing the doubts.

For first question, I think it is found by experiment, I don't know the answer.
For question 2, think of a magnetic dipole, the B flux in between N and S is from S to N, but for the flux going outside, will go from N to S, but for electric dipole, the flux always go from + to -. This tells you why magnet is closed loops and electric field is open loops.

 

[sunmaggot]

I would like to add this as a question, a wire of current I is moving in +y axis and a electron is revolving at a distance of x m along +k direction, does it feel any magnetic force, and what if it was spinning along +y direction.
Thanks in advance for clearing the doubts.

the electron will not feel magnetic force if the electron perfectly follow the path. However, any little deviation will cost the electron to move down and up because of magnetic force, but this should not be a concern in your question.

 

[stedwards]

Q2.Why are magnets always in dipoles, and further, why magnetic fields form closed loops, while electric fields are open loops.

An electric charge is a source of the electric field; Gauss's Law. $\rho = \epsilon \nabla \cdot E$. Gauss's Law for magnetims says $0= \nabla \cdot B$. This says, the divergence of the magnetic field is zero out of any region.

This doesn't say a lot. But if the electric and magnetic fields are expressed in terms of a more fundamental vector quantity $A$, where $B= \nabla \times A$, then it is a mathematical identity that $\nabla \cdot B$ must be zero. $\nabla \cdot \nabla \times A=0$ for any $A$.

 

[Khashishi]

A1. Electron spin is a relativistic quantum mechanical effect which isn't actually an electron spinning in the classical sense. If you haven't studied quantum mechanics, there's no easy way to understand it, so you are just going to have to accept it. Anyways, the relativistic version of the Schrödinger equation for spin 1/2 particles (like electrons) is the Dirac equation. The Dirac equation predicts this effect known as spin and also how it couples to the magnetic field.
This link explains it, if you are ready for it.
http://lnu.se/polopoly_fs/1.96725!PresentationGfactor.pdf
A1b. The loop of wire creates a magnetic field which has a torque on the electron, but not a force unless the electron is moving.

A2. It's because magnetic monopoles don't exist (or we haven't found them yet!). On the other hand, electric monopoles are common. A monopole is a place where field lines are converging or diverging from a point. Dipoles just form loops in the field.

 

[sunmaggot]

An electric charge is a source of the electric field; Gauss's Law. $\rho = \epsilon \nabla \cdot E$. Gauss's Law for magnetims says $0= \nabla \cdot B$. This says, the divergence of the magnetic field is zero out of any region.

using gauss's law to explain is circular argument. Gauss's law for B-field is based on the phenomenon. you cannot use the product of the phenomenon to explain.

 

[stedwards]

using gauss's law to explain is circular argument. Gauss's law for B-field is based on the phenomenon. you cannot use the product of the phenomenon to explain.

What circle? Anyway, I hit the wrong button and posted early. See the edited version of my post.

 

[sunmaggot]

What circle? Anyway, I hit the wrong button and posted early. See the edited version of my post.

circular argument: A is correct and implies B is correct. Why is A true? if you use B to prove A is correct, this is circular argument.

 

[Khashishi]

To summaggot: stedwards's answer is based on the theory of electromagnetism. It's not proven. Just not yet disproven. Circular arguments are acceptable to some extent in inductive reasoning. We (humans) created this theory of electromagnetism based on a lot of experiments. So when someone asks a question about why something happens in electromagnetism, it is sometimes better to answer in terms of the basic principles of the theory, rather than the experiments it rests on. Why? Well, the theory ties together a lot of measurements with a small number of assumptions. So the theory can be regarded as "explaining" the experiments, although the experiments are what imply the theory is correct. That's not circular. That's just how physics works.

 

[stedwards]

circular argument: A is correct and implies B is correct. Why is A true? if you use B to prove A is correct, this is circular argument.

You didn't reread. Maybe you'll understand this better.

If there exists an R⁴ fibre bundle A on the spacetime manifold of general relativity, ddA=0 (all exact forms are closed) this precludes the existence of magnetic monopoles as a mathematical identity.

 

[Prannoy Mehta]

No, I have not gone through quantum mechanics with the dept prescribed, in the text give to me by Khashidi. But I don't get one part, it experiences torque but not force. o.o Does not make sense to be. I am ignoring the electrostatic forces.

But just wanted to know, the school provided text states, if we pick a reference frame as such to travel at the same speed as the electron near a current carrying conducting wire, there will be only a electrostatic force, despite the wire being neutral. These things, are weird. I cannot seem to understand these things, mechanics was much easier to understand.

 

[Khashishi]

But the wire isn't neutral from the electron's rest frame. With mechanics, you can often ignore relativistic effects if you are working with slow moving bodies. But electromagnetism and relativity go together, and you can't often ignore the effects of relativity.