Suppose we have an infinite line of charge such that the linear charge distri- bution is given by -a² /a² X(x) : a where a is a constant with dimension of length. We can determine the electrostatic...

Extracted text: Suppose we have an infinite line of charge such that the linear charge distri- bution is given by -a² /a² X(x) : a where a is a constant with dimension of length. We can determine the electrostatic potential some perpendicular distance z above the line to be (in SI units) 20 V(2) = e-a²/a? xp: V1+ x²/z² 4T€oaz and of course we would like to evaluate the integral. (a) (paper) Make the change of variables x = aq, so that you get e-q? 2Q V (2) = roo (1) V1 +a²q² /zzdq and then with y = z/(v2a), show that this can be written as Q V(z) = -e²Ko(y²), 4περα where Ko is a modifed Bessel function. Do this by looking up integral forms of the Bessel function and compare them to Eq. (1).