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2d Coulomb and Biot-Savart laws

  1. Aug 9, 2005 #1
    I'm trying to find some sort of simple derivation of these laws in 2d, using the integral expressions of the Maxwell equations.

    For 2d Coulomb, I found this:

    Imagine a rod of infinite length along the z-axis, carrying a charge q which is uniformly divided:

    rho (the charge/volume) = lambda*dz*delta(x)*delta(y)

    with dq= lambda*dz

    So, using the electrical Gauss' law, Er being the value of E in radial direction:

    eps0*Er*2*pi*r*dz = lambda*dz

    Er= lambda/(eps0*2*pi*r)

    Er =-dV/dr

    => V= -lambda/(2*eps0)*ln(r)

    So, Coulomb's law would be, with pi(r´) being the electrical charge of the surface evaluated in point r´, en ds´ being the surface that is integrated:

    V(r) = -lambda/(2*eps0)* int ( ln(r-r´) , ds´) ?

    Does that make any sense? Or is this way off the mark?

    And for the Biot-Savart law in the same manner, will the vector potential be something analogous to this thing?

    Thank you,

  2. jcsd
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