Potential due to an infinite wire is V=2kλlnr, where r is the distance from the wire. Taking the point in space P(x,y,z) Distance from wire along x-axis is rx=√y2+z2 Distance from wire along y-axis is ry=√x2+z2 Distance from wire along z-axis is rz=√x2+y2 ⇒ Potential at P due to wire along x-axis is Vx=2kλlnrx Potential at P due to wire along y-axis is Vy=2kλlnry Potential at P due to wire along z-axis is Vz=2kλlnrz ⇒ Not potential at P=V=Vx+Vy+Vz or V=2kλlnrx+2kλlnry+2kλlnrz i.e. V=2kλln(rxryrz) or V=2kλln(√y2+z2√z2+x2√x2+y2) =kλln(y2+z2)(z2+x2)(x2+y2) ⇒ For equipotential surface (x2+y2)(y2+z2)(z2+x2)= constant
