# Why do we use formula of magnetic fields for low speed charges?

I have read a answer on the site about how moving charges create magnetic fields, which included special relativity. But in low speeds occasions the effects of relativity should be incrediblely small, why we still have to consider it? Since we don't consider the effect of relativity for moving mass point moving with low speed, why consider it for magnetic fields?

I am just a sophomore student and my mother tongue is not English, i would be extremely thankful if you can use simple words. :D

• Please ask only one question. Pick the most important one and delete the rest. – Dale Mar 23 at 12:00
• @Dale: Despite the "furthermore", this seems to me to be clearly one question. The bit after the "furthermore" is not a separate question; it's an explanation of why this question is puzzling. – WillO Mar 24 at 14:00
• Yes, he/she edited it well to make it one question. I am retracting my close vote. Thanks for letting me know. I wish the system let you know when edits were made to questions you voted on. – Dale Mar 24 at 14:18

But in low speeds occasions the effects of relativity should be incrediblely small, why we still have to consider it?

The effects of relativity are very small but the effects of electromagnetism are huge! It takes only a very small excess of charge to have an enormous electrostatic effect. So although the relativistic effects are small they are not negligible for electromagnetism. They are essentially scaled up by the strength of the electromagnetic force which is roughly $$10^{36}$$ times stronger than gravity.

• Thank you for answer! But can you tell me why "It takes only a very small excess of charge to have an enormous electrostatic effect"? i am confused. – zyx Mar 23 at 14:56
• Basically the charge on an electron or a proton is many orders of magnitude larger than the mass of the electron or proton (in natural units). So it is very easy for electromagnetic forces to push particles around. – Dale Mar 23 at 15:26

1.Special Relativity doesn't fully explain the relation between electric fields and magnetic fields. It explains some occasions.

2.Relativistic effects are neglible but the electrostatic force is just very strong with little effects we can see consequences.

3.No mass and charge are not even close to similar. Charge is something fundamental (at low energies at least), mass can be converted to energy and vice-versa.

• Thanks! But can you tell me something more about the relationship between electric fields and magnetic fields? – zyx Mar 23 at 14:53
• Gauss's law: Electric charges produce an electric field. The electric flux across a closed surface is proportional to the charge enclosed. Gauss's law for magnetism: There are no magnetic monopoles. The magnetic flux across a closed surface is zero. Faraday's law: Time-varying magnetic fields produce an electric field. Ampère's law: Steady currents and time-varying electric fields (the latter due to Maxwell's correction) produce a magnetic field. – Jelly Strawberry Mar 23 at 15:06
• en.wikipedia.org/wiki/Maxwell%27s_equations – Jelly Strawberry Mar 23 at 15:07
• en.wikipedia.org/wiki/Faraday%27s_law_of_induction – Jelly Strawberry Mar 23 at 15:07
• These laws can explain the magnetic fields very well, but the nature for magnetics isn't relativity? If not, what is it? – zyx Mar 23 at 15:14

These laws can explain the magnetic fields very well, but the nature for magnetics isn't relativity? If not, what is it?

This question - which you asked in the comments - is the key to understanding magnetism. The fact that electrons (as well as protons and neutrons) have a magnetic moment was expressed in 1907 and thus long after Maxwell's equations. At the time when the magnetic dipole moment of electrons was discovered, Bohr's atomic model of the electron orbiting the nucleus was still in use, and scientists explained the magnetic moment by a rotating electron.

Today, the magnetic dipole moment of subatomic particles is defined as an intrinsic property. So if we accept the magnetic dipole as a property that exists under all circumstances, it is clear why the magnetic field has to be taken into account even for low speed electrons.