an EM wave: E = E0 sin (kx-wt) j direction + E0 cos(kx-wt) k direction B = B0 co

ID: 2106703 • Letter: A

Question

an EM wave:

E = E0 sin (kx-wt) j direction + E0 cos(kx-wt) k direction

B = B0 cos(kx-wt) j direction - B0 sin (kx-wt) k direction

a. show that E and B are perpendicular to each other at all times

b. For this wave, E and B are in a plane parallel to they yz plane. Show that the wave moves in a direction perpendicular to both E and B.

c. at any arbitrary choice of position and time, show that the magnitude of E and B always equal E0 and B0.

d. What is the angle between E and the positive z-axis at x=y=z=0 and at time = 0 , time = PI/2w, time = Pi/w.

Discribe the motion of the E-field as time passes

a) consider dot product

E*B = E0 sin(kx-wt) B0 cos(kx-wt) - E0 cos(kx-wt) B sin(kx-wt) = 0

since 0 they are perpindicular

b) wave moves in the +x direction since with increaseing t to keep kx-wt constant x has to increase

c) mag of E = sqrt(E*E) = sqrt( E0^2 sin^2 + E0^2 cos^2)

but sin^2 + cos^2 = 1

= sqrt(E0^2) = E0

same thing for B

b) to find angle E*z = E0 cos theta

cos theta = cos(kx-wt)

theta = kx - wt = - wt

t = 0, theta = 0

t=pi /2w, theta = -pi/2

t= pi/w, theta = -pi

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