We know that when an electron moves at a velocity,it produces magnetic field.
My question is how strong the magnetic field will be if electron moves at a velocity $v$ or with an acceleration $a$ and by what formula.
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$\begingroup$ For the vectors $\,\mathbf E,\,\mathbf B\,$ of the electromagnetic field produced by an arbitrary moving point charge see equations (01.1),(01.2) in my amswer here : Electric field associated with moving charge, equations (14.14),(14.13) extracted from J.D.Jackson's $^{\prime}$Classical Electrodynamics$^{\prime}$, 3rd Edition. $\endgroup$– FrobeniusCommented Jan 23, 2022 at 7:29
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$\begingroup$ For the vectors $\,\mathbf E,\,\mathbf B\,$ of the electromagnetic field produced by an uniformly moving point charge see the relativistic equations (01a),(01b) in my amswer here : Magnetic field due to a single moving charge, equations produced by Lienard-Wiechert potentials. In this same answer for the vector $\,\mathbf B\,$ from a slowly moving point charge see the non-relativistic equation (02) produced by the Biot-Savart Law. $\endgroup$– FrobeniusCommented Jan 23, 2022 at 7:41
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1 Answer
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You can use this equation to find the field produced by a moving charge (or an electron in this specific case) with this equation:-
\begin{equation} \mathbf{B}\boldsymbol{=}\dfrac{\mu_{0}}{4\pi}\dfrac{q\left(\boldsymbol{\upsilon}\boldsymbol{\times}\mathbf{\hat{r}}\right)}{r^2} \end{equation} And In the case in which the velocity is time dependent then you will have to substitute the term $v$ with the function of time and you will get the variable magnetic field strength with the variable velocity.
I suggest you to please have a look at this article.
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$\begingroup$ why mass $m$ is used in the formula? What will be the SI unit of that formula? $\endgroup$ Commented Jan 23, 2022 at 10:37
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$\begingroup$ @KaushikKumbhat that is not only $m$, I've written $mu$ "mu" is a Greek letter, and here it's used to denote the term know as permeability of air or vacuum, that symbol was not available in my keyboard so I was unable to put the actual symbol. But I'll rectify this issue soon! $\endgroup$ Commented Jan 23, 2022 at 10:59
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$\begingroup$ Okay that's done you can go through the answer now! $\endgroup$ Commented Jan 23, 2022 at 11:03
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$\begingroup$ @Frobenius I'm curious to know about what your edit mean! $\endgroup$ Commented Jan 23, 2022 at 12:20
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$\begingroup$ You're right. I don't realize, because of the small size font, that you have the unit vector $\mathbf{\hat{r}}$ and not $\mathbf r$. So, I edit your equation to be more clear. If you don't agree I'll turn it as you post it initially.. $\endgroup$ Commented Jan 23, 2022 at 12:26