Answer Happy

Problem 8: In electromagnetic scattering by an infinite cylinder of radius a, under certain conditions, the time-harmonic electric field is given by E= u(2,0) Ĉ, where u satisfies the Helmholtz wave equation = = 0<p <a, Ο <φ < 2π a²u 1ди 1 02u + + + k?u= 0, др? р др p2 202 u(0,0) is finite, u(a,0) = eika coso ulp,0) = u(p,27), us (p, 0) иф (р, 2п) where k is a constant. Solve it. Hint: Use the generating function of the Bessel function when obtaining the unknown coefficient.