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Lorentz force on a charged ... Position vector r is a point to calculate the electric field ... ISBN 978-0-521-57507-2. A. Halpern (1988). 3000 Solved Problems in ...
In the image, the vector F 1 is the force experienced by q 1, and the vector F 2 is the force experienced by q 2. When q 1 q 2 > 0 the forces are repulsive (as in the image) and when q 1 q 2 < 0 the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.
These equations taken together are as powerful and complete as Maxwell's equations. Moreover, the problem has been reduced somewhat, as the electric and magnetic fields together had six components to solve for. [1] In the potential formulation, there are only four components: the electric potential and the three components of the vector potential.
In the differential form formulation on arbitrary space times, F = 1 / 2 F αβ dx α ∧ dx β is the electromagnetic tensor considered as a 2-form, A = A α dx α is the potential 1-form, = is the current 3-form, d is the exterior derivative, and is the Hodge star on forms defined (up to its orientation, i.e. its sign) by the ...
The electric field was formally defined as the force exerted per unit charge, but the concept of potential allows for a more useful and equivalent definition: the electric field is the local gradient of the electric potential. Usually expressed in volts per metre, the vector direction of the field is the line of greatest slope of potential, and ...
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 ...
The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics.The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).
The most important aspect of the EFIE is that it allows us to solve the radiation/scattering problem in an unbounded region, or one whose boundary is located at infinity. For closed surfaces, it is possible to use the Magnetic Field Integral Equation or the Combined Field Integral Equation, both of which result in a set of equations with ...