The Potential
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The Potential of a Localized Charge Distribution
Setting the reference point an infinity, the potential of a point charge q at the origin isV(r) = -1/4πε0 ∫ q/r2 dr’ = 1/4πε0 q/r’ | = 1/4πε0 q/r’ q/r
The potential of a point charge q is V(P) = 1/4πε0 q/r
Suppose that we have some electric charges, q1, q2, q3, …. (Call them source charges)
By the principle of superposition, the potential at any point is the sum of the potentials due to all the source charges separately. So the potential of a collection of charges is
V(P) = 1/4πε0 ∑(i=1)^nqi/ri
Suppose charge is distributed throughout some finite volume with a known charge density ρ (C/m3). For a continuous distribution,
V(P) = 1/4πε0 ∫ ρ/r dτ
Eq. (3) tells us how to compute V when we know ρ.
The integrals analogous to Eq (3) for line and surface charges are
1/4πε0 ∫ λ/r dl and 1/4πε0 ∫ σ/r da
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