A hemispherical wire has a linear charge density theta C cos

A hemispherical wire, has a linear charge density, ?(theta)= C cos^2(theta), where C is a constant. find the electrical potential at the center point of the hemispherical wire, a distance, r, from the charge density. put you solution in terms of C, r, ?, and numerical constants if needed.

Solution

the charge density

linear charge density = total charge Q / length of the wire ( 2 * r)

C * cos^2(theta) = Q* 2*r

Q = C* cos^2(theta) / 2 * r

so the electrical potential at the center point of the hemispherical wire is

V = k Q / r

V = k * C * cos^2(theta) / 2 * r^2