Function Conjunction → Functions composed of Physical Expressions

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Functions for a point charge q

The electric scalar potential φ at (r,t) due to a point charge q at (r,t) is:

φ(r,r)=q4π ϵ0constant×1|rr|proximity

The magnetic vector potential A at (r,t) due to a point charge q which had a velocity drdt at (r,t) is:

A(r,r)=φ(r,r)×1c2constant×drdtdislocation

A(r,r)=μ0 q4πconstant×1|rr|proximity×drdtdislocation

Functions for an ordered pair of point charges (q,q)

A charge q subject to an electric scalar potential φ at (r,t) due to a point charge q at (r,t) has an electric potential energy of:

qφ(r,r)=qq4π ϵ0constant×1|rr|proximity

A charge q subject to a magnetic vector potential A at (r,t) due to a point charge q which had a velocity drdt at (r,t) has a potential momentum of:

qA(r,r)=φ(r,r)×qc2constant×drdtdislocation
qA(r,r)=μ0 qq4πconstant×1|rr|proximity×drdtdislocation

Lorentz Force for (q,q)

The Lorentz Force between charges (q,q) can be derived from the scalar potential φ and the vector potential A.

A charge q which has a velocity of v at (r,t) will experience a Lorentz force due to a point charge q at (r,t) of:

F=q[E+v×B]

The electric field E is:

E=φAt

The magnetic field B is:

B=×A

The Lorentz Force can be expressed directly in terms of the potentials:

F=q[φAt+v×(×A)]

See also

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