A plane electromagnetic wave traveling in the positive direction of an x axis in

Question

A plane electromagnetic wave traveling in the positive direction of an x axis in vacuum has components Ex = Ey = 0 and Ez = (5.0 V/m) cos[(p × 1015 s-1)(t - x/c)].(a) What is the amplitude of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate (enter 1 for x axis, 2 for y axis and 3 for z axis)? (c) When the electric field component is in the positive direction of the z axis at a certain point P, what is the direction of the magnetic field component there (enter 1 for x axis, 2 for y axis and 3 for z axis. For opposite direction use minus sign)? Assume that the speed of light is 2.998*108 m/s.

Explanation / Answer

according to given problem , we have x, y , z - components of the electeomagnetic waves is       Ex = Ey = 0 and Ez = (5 V/m) cos[(*1015 s-1)(t - x/c)] here , maximum electric field Em = 5 V/m a) the amplitude of the magnetic field is                 Bm = Em/c                       = (5 V/m) / ( 2.998*108 m/s)                       = 1.667*10-8 T b) from given problem , the waves oscillates in z-direction and its travels in +ve x-direction. so , Bx = Bz = 0 therefore , the oscillation of the magnetic field is parallel to the y-axis. c) electromagnetic wave propagation is determined by E*B.                 ( * = cross product) if the electric field component is in the positive direction of the z axis , then the magnetic field is in the y-axis (direction)      By = Bm cos[(*1015 s-1)(t - x/c)]            = (1.667*10-8 T) cos[(*1015 s-1)(t - x/c)] b) from given problem , the waves oscillates in z-direction and its travels in +ve x-direction. so , Bx = Bz = 0 therefore , the oscillation of the magnetic field is parallel to the y-axis. c) electromagnetic wave propagation is determined by E*B.                 ( * = cross product) if the electric field component is in the positive direction of the z axis , then the magnetic field is in the y-axis (direction)      By = Bm cos[(*1015 s-1)(t - x/c)]            = (1.667*10-8 T) cos[(*1015 s-1)(t - x/c)]

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