is then Now consider the case of cylinder with the same linear current density as the conductor of arbitrary cross-section. It is also well known that the potential at any point on its surface, which is also equal its average potential, is Equating and yields Exponentiation of both side leads to the formula for the equivalent radius. The formula for the equivalent radius provides consistent results. If the conductor cross-section dimensions are scaled by a factor , the equivalent radius is scaled by . Also, the equivalent radius of a cylindrical conductor is equal to the radius of the conductor. References Antennas (radio)