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Consider a long, thin wire of charge and length .To calculate the average linear charge density, ¯, of this one dimensional object, we can simply divide the total charge, , by the total length, : ¯ = If we describe the wire as having a varying charge (one that varies as a function of position along the length of the wire, ), we can write: = Each infinitesimal unit of charge, , is equal to ...
Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m −1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative. Like mass density, charge density can vary with
Here, k e is a constant, q 1 and q 2 are the quantities of each charge, and the scalar r is the distance between the charges. The force is along the straight line joining the two charges. If the charges have the same sign, the electrostatic force between them makes them repel; if they have different signs, the force between them makes them attract.
An electric field (sometimes called E-field [1]) is the physical field that surrounds electrically charged particles.Charged particles exert attractive forces on each other when their charges are opposite, and repulse each other when their charges are the same.
The law was first [1] formulated by Joseph-Louis Lagrange in 1773, [2] followed by Carl Friedrich Gauss in 1835, [3] both in the context of the attraction of ellipsoids. It is one of Maxwell's equations, which forms the basis of classical electrodynamics. [note 1] Gauss's law can be used to derive Coulomb's law, [4] and vice versa.
The wire has a linear density ρ (M/L) and is under tension s (LM/T 2), and we want to know the energy E (L 2 M/T 2) in the wire. Let π 1 and π 2 be two dimensionless products of powers of the variables chosen, given by = =. The linear density of the wire is not involved. The two groups found can be combined into an equivalent form as an equation
Position vectors r and r′ used in the calculation. Jefimenko's equations give the electric field E and magnetic field B produced by an arbitrary charge or current distribution, of charge density ρ and current density J: [2]
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...