Combining the electromagnetic wave equation and Ohm's law produces ∇ ∇ 2 J ( r ) + k 2 J ( r ) = ∂ ∂ 2 ∂ ∂ r 2 J ( r ) + 1 r ∂ ∂ ∂ ∂ r J ( r ) + k 2 J ( r ) = 0. The solution to this equation is, for finite current in the center of the conductor, J ( r ) = C J 0 ( k r ) , where J 0 is a Bessel function of the first kind of order 0 and C is a constant phasor. To satisfy the boundary condition for the current density at the surface of the conductor, J ( R ) , C must be J ( R ) J 0 ( k R ) . Thus, J ( r ) = J ( R ) J 0 ( k r ) J 0 ( k R ) .