Why does a moving point charge does not produce a magnetic field? why does it always have to be a current? I am a high-school student with knowledge of basic calculus.
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Related : Electric field associated with moving charge. – Frobenius Aug 16 '21 at 11:38
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A moving point charge does produce a magnetic field (along with an electric field). After all a current is essentially a collection of moving point charges.
The magnetic field of a point charge moving with a constant velocity $\vec v$ can be approximately determined from Biot-Savart's law or more accurately by Maxwell's equations. In vaccum it is given by: $$\vec B = \frac{\mu_0}{4\pi}.\frac {q \vec v \text{ x } \hat r}{r^2}$$ provided $v \ll c$ ; the speed of light
Hope this helps.
Cross
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This is not strictly correct. Biot-Savart applies to steady-state currents and a single charge is not that. – IcyOtter Aug 16 '21 at 09:03
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@IcyOtter, Biot-Savart's law applies to current elements and these can easily be modified to a single charge by substituing $$I = n_v .q.A.v$$ (from Drude's model of electrical conduction) with $n_v A.ds = 1$ to give the desired result. – Cross Aug 16 '21 at 09:24
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That's not what your post says. You are saying that the B field from a point charge in vacuum is given by the expression you provided. That is not correct. A B-field of a point charge cannot be obtained from B-S law. It must include retardation effects: https://en.wikipedia.org/wiki/Liénard–Wiechert_potential . In the limit v << c, B-S is a decent approximation. – IcyOtter Aug 16 '21 at 09:25
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