Faraday's Paradox (1 Viewer)
wizzkids
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Yes, I will try to explain why this is not really a paradox.
Firstly, the cylindrical magnet produces a radial and symmetrical magnetic field, and it does so whether the magnet is rotating or not. Don't get confused by Faraday's description of his imaginary "lines of magnetic flux" because that's why he got into a muddle and could not adequately explain why this is NOT a paradox.
So we have this established radial magnetic field, and its distribution in space is the same whether the magnet rotates or not. So, the correct way to visualise the magnetic field is that it has a stationary field relative to the observer. The paradox only appears if you try to imagine Faraday's imaginary lines of magnetic flux moving through space, which is incorrect.
Next we consider the conducting disk. All charged particles that move in a magnetic field experience a Lorentz force, and if the charged particles are stationary they do not experience the Lorentz force. The induced emf in the disk is directed from the axle to the rim, so it is a radial emf that is induced. The induced emf is generated all the way around the rim of the disk, but only when the disk is rotating relative to the frame of reference of the observer. Hence, the conducting disk, containing the charged particles, must be in motion before there can be any induced emf.
Do you see now why it is not a paradox?
Firstly, the cylindrical magnet produces a radial and symmetrical magnetic field, and it does so whether the magnet is rotating or not. Don't get confused by Faraday's description of his imaginary "lines of magnetic flux" because that's why he got into a muddle and could not adequately explain why this is NOT a paradox.
So we have this established radial magnetic field, and its distribution in space is the same whether the magnet rotates or not. So, the correct way to visualise the magnetic field is that it has a stationary field relative to the observer. The paradox only appears if you try to imagine Faraday's imaginary lines of magnetic flux moving through space, which is incorrect.
Next we consider the conducting disk. All charged particles that move in a magnetic field experience a Lorentz force, and if the charged particles are stationary they do not experience the Lorentz force. The induced emf in the disk is directed from the axle to the rim, so it is a radial emf that is induced. The induced emf is generated all the way around the rim of the disk, but only when the disk is rotating relative to the frame of reference of the observer. Hence, the conducting disk, containing the charged particles, must be in motion before there can be any induced emf.
Do you see now why it is not a paradox?
wizzkids
Well-Known Member
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- Jul 13, 2016
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- 1998
Good question. The magnetic field strength, its flux and its direction, is static. It does not vary. Remember, the equations for electromagnetic induction only refer to the rate of change of the magnitude of the B-field. Anyway, in the op above, the magnetic field vector does not change. As I said before, don't get misled by Faraday's imaginary lines of magnetic flux moving through space - they don't exist. That is the limitation of Faraday's model for the magnetic field.