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1. This course deals with Maxwell's equations. In some cases, these four equations are given by 7 ·Ē = 0, ỹ . B = 0, (1) 7 ×Ẻ = – 7 × B = 1 dỂ c² Ət where E and B are the electric and magnetic field, respectively, and c is the speed a light in vacuum (a constant). a) Using Cartesian coordinates, show that Ē(x, y, z, t) B(x, y, z, t) 2 Eo cos T cos "" sin wt , (3) = Bo [-x cos ( sin () + ŷ sin () cos ()] cos wt , (4) CoS satisfy all four of Maxwell's equation provided that the constants satisfy w = v V2n c/L, Bo = Eo/V2c.

1. This course deals with Maxwell's equations. In some cases, these four equations are given by 7 ·Ē = 0, ỹ . B = 0, (1) 7 ×Ẻ = – 7 × B = 1 dỂ c² Ət where E and B are the electric and magnetic field, respectively, and c is the speed a light in vacuum (a constant). a) Using Cartesian coordinates, show that Ē(x, y, z, t) B(x, y, z, t) 2 Eo cos T cos "" sin wt , (3) = Bo [-x cos ( sin () + ŷ sin () cos ()] cos wt , (4) CoS satisfy all four of Maxwell's equation provided that the constants satisfy w = v V2n c/L, Bo = Eo/V2c.

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1. This course deals with Maxwell's equations. In some cases, these four equations are given by V.E = 0, V.B = 0, (1) 1 ĐỂ V × B (2) at c2 Ət where E and B are the electric and magnetic field, respectively, and c is the speed a light in vacuum (a constant). a) Using Cartesian coordinates, show that Ē(x, y, z, t) î Eo cos T cos TY sin wt, (3) COS B(x, y, z, t) = Bo [-x cos () sin () + ŷ sin () cos ()] cos wt, Во TY) cos wt, (4) COS L satisfy all four of Maxwell's equation provided that the constants satisfy w = v2n c/L, Bo = Eo//2c. b) Using cylindrical coordinates, find the condition under which Vo Ē(r, 9, 2) cos(kz – wt), (5) = r r log(b/a) Vo B(r,9, 2) cos(kz – wt) , (6) rclog(b/a) satisfy all found Maxwell's equations. Here, a, b, Vo, and k are constants.
Transcribed Image Text:1. This course deals with Maxwell's equations. In some cases, these four equations are given by V.E = 0, V.B = 0, (1) 1 ĐỂ V × B (2) at c2 Ət where E and B are the electric and magnetic field, respectively, and c is the speed a light in vacuum (a constant). a) Using Cartesian coordinates, show that Ē(x, y, z, t) î Eo cos T cos TY sin wt, (3) COS B(x, y, z, t) = Bo [-x cos () sin () + ŷ sin () cos ()] cos wt, Во TY) cos wt, (4) COS L satisfy all four of Maxwell's equation provided that the constants satisfy w = v2n c/L, Bo = Eo//2c. b) Using cylindrical coordinates, find the condition under which Vo Ē(r, 9, 2) cos(kz – wt), (5) = r r log(b/a) Vo B(r,9, 2) cos(kz – wt) , (6) rclog(b/a) satisfy all found Maxwell's equations. Here, a, b, Vo, and k are constants.
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