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The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q m (Wb) = μ 0 q m (Am).
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior.Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation: = where E is the electric field caused by the charge on the conductor and is the permittivity of the free space.
In applications one also has to describe how the free currents and charge density behave in terms of E and B possibly coupled to other physical quantities like pressure, and the mass, number density, and velocity of charge-carrying particles. E.g., the original equations given by Maxwell (see History of Maxwell's equations) included Ohm's law ...
The multipole expansion circumvents this difficulty by expanding not E or B, but r ⋅ E or r ⋅ B into spherical harmonics. These expansions still solve the original Helmholtz equations for E and B because for a divergence-free field F, ∇ 2 (r ⋅ F) = r ⋅ (∇ 2 F). The resulting expressions for a generic electromagnetic field are:
Consider two small spheres of mass and same-sign charge , hanging from two ropes of negligible mass of length . The forces acting on each sphere are three: the weight m g {\displaystyle mg} , the rope tension T {\displaystyle \mathbf {T} } and the electric force F {\displaystyle \mathbf {F} } .
Proof that the formulations of Gauss's law in terms of free charge are equivalent to the formulations involving total charge. In this proof, we will show that the equation = is equivalent to the equation = Note that we are only dealing with the differential forms, not the integral forms, but that is sufficient since the differential and ...
m e is the electron mass (approximately 9.1 × 10 −31 kg). The Hall parameter value increases with the magnetic field strength. Physically, the trajectories of electrons are curved by the Lorentz force. Nevertheless, when the Hall parameter is low, their motion between two encounters with heavy particles (neutral or ion) is almost linear. But ...