Question

A magnetic field vibrates in the direction y = 2x. if the wave propagates in the negative z axis. What is the electric field direction?

a) x = 2
b) z =- x
c) x =- 2y
y =- 2x

thanku 4 ur help!

Answer 1

i think y=-2x as this will give their combined perpendicular direction as -z axis

Answer 2

Maxwell's equation in a vacuum imply that the electric and magnetic field oscillate perpendicular to one another. They also oscillate perpendicular to the direction of propagation. So you know the wave propagates in the z direction so the magnetic and electric fields are confined to oscillate in the x-y plane.

Thus the answer must be x=-2y as this is at 90 degrees to y=2x.

Proof:

Take some vector in the y = 2x direction: (1 2) and some vector in the x=-2y direction (1 -1/2). Note my notation for the vectors are ( x y ). Take the dot product of these two vectors:

(1 2) dot (1 -1/2) = 1 - 1= 0. Therefore these two vectors are perpendicular. Therefore the two lines are perpendicular.