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Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field , following the Biot–Savart law , and the other wire experiences a magnetic force as a consequence, following ...
As of the 2019 revision of the SI, the ampere is defined by fixing the elementary charge e to be exactly 1.602 176 634 × 10 −19 C, [6] [9] which means an ampere is an electric current equivalent to 10 19 elementary charges moving every 1.602 176 634 seconds or 6.241 509 074 × 10 18 elementary charges moving in a second.
Factor () Value Item 10 −19: 160 zA Current flow of one electron per second : 10 −12: 1-15 pA Range of currents associated with single ion channels [calcium (1 pA), sodium (10-14 pA), potassium (6 pA)] as measured by patch-clamp studies of biological membranes
Equation [D], with the μv × H term, is effectively the Lorentz force, similarly to equation (77) of his 1861 paper (see above). When Maxwell derives the electromagnetic wave equation in his 1865 paper, he uses equation [D] to cater for electromagnetic induction rather than Faraday's law of induction which is used in modern textbooks. (Faraday ...
The first equation listed above corresponds to both Gauss's Law (for β = 0) and the Ampère-Maxwell Law (for β = 1, 2, 3). The second equation corresponds to the two remaining equations, Gauss's law for magnetism (for β = 0) and Faraday's Law (for β = 1, 2, 3).
Importantly, Gauss's force law is a significant generalization of Ampere's force law, since moving point charges do not represent direct currents. In fact, today Ampere's force law is no longer presented in its original form , as there are equivalent representations for direct currents such as the Biot-Savart law in combination with the Lorentz ...
The force obtained in the case of a current loop model is = (), where the gradient ∇ is the change of the quantity m · B per unit distance, and the direction is that of maximum increase of m · B. To understand this equation, note that the dot product m · B = mB cos( θ ) , where m and B represent the magnitude of the m and B vectors and θ ...