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an electron has its own electric field around it when it's at rest . but according to Biot Savart law it's stated that a magnetic field is created around a current carrying conductor . current is defined as the rate of flow of charge. my question is an static electron has an electric field around it but when the same electron moves in conductor how a magnetic field is created around it ?

MIT 8.01 Physics I Classical Mechanics, Fall 1999
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what's the difference? field is field - no matter what additions like magnetic or electric you add to it. it's like having a small force and a larger one and telling that they're totally different from each other. the magnetic field as you call it is the result of the electron moving in the conductor which results in the conductor trying to resist - byproduct: a field - this acts upon the electron which then also tries to resist against this field ...which produces the electric field around the electron - this then again has an additional effect on the conductor which again reacts with an additional field (but the effect dries out so that you get the result you can measure (with a certain coarseness of course)).
The electric and magnetic field are different aspects of the same thing. What one frame of reference may see as pure electric field, may be seen by a moving frame of reference (with respect to the charge) by both electric and magnetic field. An interesting problem for you is to try to explain the following: "imagina that you arrange a field configuration such that you can put two electric charged particles at rest (in an unstable equilibrium). Well that seems fine doesn't it? Now change your frame of reference to one that is moving perperdincular to the line between the charges. Io and behold! Now there is a magnetic force attracting them, so they should move, shouldn't they? The equilibrium broken, for the forced would be unbalanced. But that doesn't happen, because you didn't changed the physics, you just changed the frame of reference. Try to explain this. If you manage to do so, then you'll have undesrtand a profound characteristic of EM fields.
When the charge is moving, it generates a magnetic field IN ADDITION to the electric field. Unfortunately a full answer to andrefb's conundrum requires an understanding of relativity, wherein electric fields and magnetic fields are revealed as being components of a single object - the electromagnetic field tensor. A bit beyond the usual introductory physics course syllabus :-(

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