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d is the thickness of the sheet or diameter of the wire (m), f is the frequency (Hz), k is a constant equal to 1 for a thin sheet and 2 for a thin wire, ρ is the resistivity of the material (Ω m), and; D is the density of the material (kg/m 3).
The area swept out by a vector element dl of a loop ∂Σ in time dt when it has moved with velocity v l. The proof of this is a little more difficult than the first term; more details and alternate approaches for the proof can be found in the references. [28] [29] [30] As the
where is the length of the conductor, measured in metres [m], A is the cross-section area of the conductor measured in square metres [m 2], σ is the electrical conductivity measured in siemens per meter (S·m −1), and ρ is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-metres (Ω·m ...
The electrical resistance of a uniform conductor is given in terms of resistivity by: [40] = where ℓ is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr 2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
[1] [2] [3] For example, if a 1 m 3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m. Electrical conductivity (or specific conductance) is the reciprocal of electrical resistivity. It represents a material's ability to conduct ...
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. [1]: 2 [2]: 622 The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor.
where is the length of the conductor, measured in metres (m), A is the cross-sectional area of the conductor measured in square metres (m 2), σ is the electrical conductivity measured in siemens per meter (S·m −1), and ρ is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-metres (Ω ...
Nevertheless, it will be a Galilean transformation to a very good approximation, at velocities much less than the speed of light. Unprimed quantities correspond to the rest frame of the magnet, while primed quantities correspond to the rest frame of the conductor. Let v be the velocity of the conductor, as seen from the magnet frame.