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I know that the magnetic field of a moving charge is: $$\vec B=\frac {\mu_0 q \vec v \times \hat r}{4\pi r^{2}}.$$ I want to know how this formula was derived, so that I can get a better understanding.

Thomas Fritsch
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nkucuk
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  • Hi and welcome to physics SE. Please, use laTex notation for formulae. It's about writing them in between of dollar symbols, and laTex commands inside. See here: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – FGSUZ Feb 02 '19 at 11:23
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    Before you ask, you should do some research on your own. Have you read about Biot-Savart's law? – FGSUZ Feb 02 '19 at 11:25
  • Before I ask, I actually did some research on my own.I couldn't find the proof. I also read about Biot-Savart. I thought Biot-Savart is used when you have a current carrying wire and a point P at a distance. I was asking about point charges like a single electron or a proton. Is it still applicable? – nkucuk Feb 02 '19 at 11:38
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    The Biot - Savart law is correct to compute the field of a moving charge in the non relativistic limitc. In the general case, you have to use the Liénard–Wiechert potential. You can take a look at https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential – Vincent Fraticelli Feb 02 '19 at 12:34
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    Related (if not duplicate) : Magnetic Field due to a single moving charge – Frobenius Feb 02 '19 at 12:39
  • Would this be better on HSM? – BioPhysicist Feb 02 '19 at 12:45
  • Thanks a lot everyone, Liénard-Wiechert is what I was looking for. All is clear now. – nkucuk Feb 02 '19 at 12:56

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