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Unformatted text preview: tial close to the wire, or by doing a brute force integration using
the electrostatic force law and the charge on the wire.
By superposition, if we now have two wires located at z = c and z = -c, and
oppositely charged (positive at c and negative at -c), we obtain
F(z) = A[Ln(z-c) - Ln(z+c)]
This gives the real part (actual potential) as
∞(z) = A lnÔ Ô
The equipotentials are therefore given by
Ô Ô = constant
If we use a little coordinate geometry, and find all (x, y) whose distance from one point =
constant time its distance from another, we get the equation of a circle (or in one special
case when the constant is 1, a line). This gives the equipotential lines as shown: 30 - + Question What is the significance of the conjugate potential?
Answer. Since ∞ and § are conjugate,
In other words, Ô ∞ and Ô § are orthogonal. However, since these gradients are
themselves orthogonal to the lines ∞ = const and §...
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