Soln11 - EM Waves

Soln11 - EM Waves - 8B Worksheet Answers 11. EM Waves 1. a)...

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8B Worksheet Answers 11. EM Waves 1. a) The wave is propagating in the " ˆ x -direction. b) The wave is transverse : The electric and magnetic fields are oriented in a direction perpendicular to the direction of propagation. c) E 1 = E 2 = E 4 > E 3 = 0 d) Yes: Points 1, 2, and 4 all have the same x and we are evaluating E at the same time, so the fields are identical. e) B 1 = B 2 = B 4 > B 3 = 0 f) Yes: Points 1, 2, and 4 all have the same x and we are evaluating B at the same time, so the fields are identical. 2. a) The electric field points vertically up (see green vector in the figure for part (b)) for reasons explained in part (c). b) Electric Field: Blue Magnetic Field: Red Note: Only a few vectors are explicitly shown. The sinusoidal waves you see are the ‘vector envelope’ of the wave along the axis: That is, if we were to draw field vectors for points along the axis, then drew a curve connecting all of their tips together, we would get the ‘vector envelope’. c) Point R is 2 d = λ / 2 away from P , so the B -field has had its phase (the angle in the cosine or sine when we write out the form of B ) advance by π . Adding a π in the argument of a sine or cosine has the effect of making the sine or cosine negative - i.e.
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sin( θ + π ) = -sin( ). Therefore, r B ( R ) = " r B ( P ) = " r B 1 , so vector C represents the magnetic field at R . d) Point T is 4 d = λ away from P , so the E -field has had its phase advance by 2 π , which means the E -field at T is the same as the E -field at P . We know that the electric field at P must be pointing either vertically up or down, since the vector r E must be both perpendicular to the vector
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Soln11 - EM Waves - 8B Worksheet Answers 11. EM Waves 1. a)...

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