Two long parallel wires run along the axis direction

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics

The Boundary-Value Problem, Ch Cylindrical geometry, edges, and what a field does to a dipole

Problem

Two long parallel wires run along the

z

axis direction, separated by

d = 2.0\,\mathrm{cm}

, carrying line charge densities

+\lambda

and

-\lambda

with

\lambda = 4.0\,\mathrm{nC\,m^{-1}}

. Their midpoint is taken as the origin of a cylindrical coordinate

s

, with

\phi

measured from the direction of the

+\lambda

wire. At a field point far from the wires,

s = 50\,\mathrm{cm}

from the midpoint, at

\phi = 30^\circ

, the potential is well approximated by the leading two-dimensional multipole term

V = \dfrac{\lambda d\cos\phi}{2\pi\varepsilon_0 s}

. Find

V

there.

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