Question

ou are given the following E F1e a) Use Faraday's Law to find the H field associated with this in time domairn b) Then use Ampere's law to find the E field, to verify that you answer is OK. c) Find the power in the phasor form ExH d) Find the time domain representation of E and H for this problem 2

Answer 1

Given E^vector = E_0 e^-j beta z y^^In time domain E^vector = E_0 cos(wt - beta z)y^^(a) we know Faradays law states that nabla times E = -partial differential B/partial differential t where B = mu H implies H = B/mu Replacing with H we get nabla times E = -mu partial differential H/partial differential t therefore H = -1/mu integral (nabla times E) H = -1/mu integral contourintegral E middot dl [nabla times E = contourintegral E middot dl] H = E_0/mu cos(wt - beta z) (b) By amperes law we get Definition nabla times H = partial differential D/partial differential t + J Let J = 0 implies nabla times H = partial differential D/partial differential t we know D = epsilon E \r\n therefore E = integral contour H middot dl E = -epsilon E_0/mu cos(wt - beta z) (c) we know P = 1/2 E^vector times H^vector^* E^vector = E_0 e^-j beta z, H^vector = E_0/mu