2. 4/6 points | Previous Answers YF14 32. P008. An electromagnetic wave of wavel
ID: 1780791 • Letter: 2
Question
2. 4/6 points | Previous Answers YF14 32. P008. An electromagnetic wave of wavelength 458 nm is traveling in vacuum in the-z-direction. The electric field has amplitude 2.65 × 10-3 V/m and is parallel to the x-axis. (a) What is the frequency? Hz 65E14 (b) What Is the magnetlc-fleld ampltude? 8-8.83E-12 T (c) Write the vector equations for E(z, t) and B(z, t). (Use the following as necessary: z and t. Let the units of z be m and t be s.) magnitude E=| (2.65R-3).cos( (1.377 )m+(4.111:15 )s)X E(z, t) v/m direction #x-direction Btz, c) magnitude 8-(8.83E 12)((1.3T)(4.11F15)/x T direction -y-direction 3. -15 points YF14 32 P011. An electromagnetic wave has an electric field given by Ey, t)-(2.85 x 105 v/m)k sinky 1.254 x 1013 rad/s)t]). (a) In which direction is the wave traveling? +x-direction x-direction +y-directionExplanation / Answer
(3) Last option '-y - direction' is the correct answer.
Explanation:
A plane wave moving in the positive y-direction can be represented by:
z(y,t) = zmax sin (ky - t)
The 'z' can be any oscillating wave parameter, such as magnetic field strength, (B), electric field strength (E), height of water, etc.
k (the wave number) is 2/ where is the wavelength.
(angular frequency) is 2/T where T is the period. (It follows that =2f, where f is the 'normal' frequency.)
Take a simple example: z = sin (y - t). Here ymax =1, k = 1 and =1.
Take time=0, this gives y= sin (x). Sketch this graph (simple sine curve)
Take a short time later t = 0.01. This gives z= sin (y-0.01). Sketch the curve - it gives a simple sine curve shifted to right by a small amount. The wave has moved right (+y direction).
Now repeat this using z = sin(y+t), so y =sin(y+0.01). If you work it through, you see the wave has moved left (-y direction).
z(y,t) = zmax sin(ky - t) is a wave moving in the +y direction.
z(y,t) = ymax sin(ky + t) is a wave moving in the -y direction.
In your equation E(y,t) = -(2.85 x 10^5) k sin[(ky - (1.254x10^13)t]
E is used instead of z.
The sign used in front of 'wt' is a '-' meaning that the wave is moving in the positive y-direction .
Further, the negative sign in the front means the wave is moving in the negative y - direction.
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