Vector Form of Coulomb's Law | EMTL | Electronics-Ed
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"Vector Form of Coulomb's Law.
Force is a vector quantity; it has both magnitude and direction. If point charges Q1 and Q2 are located at positions with position vectors R1 and R2, then, in vector form, Coulomb's law can be written as follows:
The force vector, F, is given by the equation: F equals one over four pi epsilon naught, times Q1 times Q2, divided by the magnitude of R12 squared, times the unit vector u12.
Where:
Epsilon naught (ε₀) is the vacuum permittivity. R12 is the displacement vector between the two charges, given by R12 equals r2 minus r1. The unit vector u12 is the vector in the direction of the line joining the charges and is calculated as u12 equals R12 divided by the magnitude of R12. In this case, the signs of Q1 and Q2 must be taken into account.
Coulomb's law is linear; if we multiply Q1 by a factor n, the force on Q2 is also multiplied by the same factor n.
Superposition also applies; the force on a charge in the presence of several other charges is the vector sum of the forces due to each individual charge acting alone."
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