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J g is mass current density or mass flux (J g = ρ g v ρ, where v ρ is the velocity of the mass flow), with SI unit kg⋅m −2 ⋅s −1; J is electric current density; G is the gravitational constant; ε 0 is the vacuum permittivity; c is both the speed of propagation of gravity and the speed of light.
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} .
The magnetic field (B, green) is directed down through the plate. The Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag force on the sheet.
The magnetic field generated by a steady current I (a constant flow of electric charges, in which charge neither accumulates nor is depleted at any point) [note 8] is described by the Biot–Savart law: [21]: 224 = ^, where the integral sums over the wire length where vector dℓ is the vector line element with direction in the same sense as ...
Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction. This is what makes it a key concept in fields such as nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), since the precession rate does not depend on the spatial orientation of the spins.
The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
The surface current density I^' is directly proportional to the remanent magnetic field B_r, which is a measure of the magnet's residual magnetization after an external magnetic field is removed. This property is crucial for the magnet's performance in applications such as magnetic levitation, where maintaining a stable and strong magnetic ...
The current density J is itself the result of the magnetic field according to Ohm's law. Again, due to matter motion and current flow, this is not necessarily the field at the same place and time. Again, due to matter motion and current flow, this is not necessarily the field at the same place and time.