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According to Biot-Savart Law, if there is a charged particle in motion, there will be a magnetic field. My question is whether the counterpart of this law also holds true, i.e. if there is a magnetic field, whether there will be a charged particle be in motion. Let me explain my question a bit more clearly. First of all I don't know whether we can have a single charge in motion and another at rest in reality. If we can have then there may be two cases:

Case 1: At time t=0 a charged particle is placed at rest at point P where B=0 and at time t>0 an external B field is created in a region R covering the point P.

Case 2: At time t=0 a magnetic field B is created in a region R. At time t>0 a charged particle is placed at rest at point P in R.

Note of Caution: The point P is chosen in such a way that there won't be any external electric field at P.

Now come to the question: Will the charged particle move? If yes, under which case?

If 'NO', whether the charged particle will absorb any energy or not?

Subhra
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2 Answers2

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Magnetic fields can be generated by particles in motion (in the classical sense). Generally, this not a requirement. For example, magnetism can arise from quantum effects, such as orbital angular momentum (you could say that this is a particle in motion in the classical sense, but quantum probabilities come into play here) and may also arise due to the spin state of a particle (not linear motion in the traditional sense).

user3814483
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The only exceptions I know arise from quantum effects. For example a charged fundamental particle with non-zero spin also creates a magnetic field. So an isolated static electron has a non-zero magnetic moment. Even though this is a purely quantum effect it can produce macroscopic fields. For example the magnetic field of a ferromagnet is due to the magnetic moments of its unpaired electrons.

If you leave aside magnetic fields originating from quantum effects then yes, the observation of a magnetic field implies a non-zero current i.e. there must be charged particles in motion. To see this look at the derivation of the Biot-Savart law from Maxwell's equations. The magnetic field is the curl of the vector potential, and this is related to the current by:

$$ \nabla^2{\bf A} = -\mu_0 {\bf J} $$

If ${\bf J}$ is zero then there is no magnetic field.

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John Rennie
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