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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.
For Faraday's first law, M, F, v are constants; thus, the larger the value of Q, the larger m will be. For Faraday's second law, Q, F, v are constants; thus, the larger the value of (equivalent weight), the larger m will be. In the simple case of constant-current electrolysis, Q = It, leading to
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.
A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by Maxwell is no longer included. The vector calculus formalism below, the work of Oliver Heaviside, [6] [7] has become standard.
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 is the angle between them. If m is in the same direction as B then the dot product is positive and the gradient points 'uphill' pulling the magnet into regions of higher B-field (more strictly larger m ...
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 ...
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 ...