Question

Suppose the electric field of an electromagnetic wave is given by the superposition of two waves: E(z,t) = E0 cos(kz - ?t) âx + E0 cos(kz + ?t) âx You may find the following identities useful: cos(kz ± ?t) = cos(kz) cos(?t) ? sin(kz) sin(?t) (a) What is the associated magnetic field B(z,t)? [7 marks] (b) Use the identity cos(a) sin(a) = (1/2) sin(2a) to show that the energy per unit area per time (the Poynting vector) transported by this wave is: S = E × B / ?0 = (E0^2 / c ?0) sin(2kz) sin(2?t) âz [9 marks] (c) What is the time-average of the Poynting vector, ?S? = (1/T) ?_0^T S(z,t) dt ? Reasoning your answer.

          Suppose the electric field of an electromagnetic wave is given by the superposition of two waves:

E(z,t) = E0 cos(kz - ?t) âx + E0 cos(kz + ?t) âx

You may find the following identities useful:

cos(kz ± ?t) = cos(kz) cos(?t) ? sin(kz) sin(?t)

(a) What is the associated magnetic field B(z,t)?

[7 marks]

(b) Use the identity cos(a) sin(a) = (1/2) sin(2a) to show that the energy per unit area per time (the Poynting vector) transported by this wave is:

S = E × B / ?0 = (E0^2 / c ?0) sin(2kz) sin(2?t) âz

[9 marks]

(c) What is the time-average of the Poynting vector, ?S? = (1/T) ?_0^T S(z,t) dt ?

Reasoning your answer.

Suppose the electric field of an electromagnetic wave is given by the superposition of two waves:

E(z,t) = E0 cos(kz - ?t) âx + E0 cos(kz + ?t) âx

You may find the following identities useful:

cos(kz ± ?t) = cos(kz) cos(?t) ? sin(kz) sin(?t)

(a) What is the associated magnetic field B(z,t)?

[7 marks]

(b) Use the identity cos(a) sin(a) = (1/2) sin(2a) to show that the energy per unit area per time (the Poynting vector) transported by this wave is:

S = E × B / ?0 = (E0^2 / c ?0) sin(2kz) sin(2?t) âz

[9 marks]

(c) What is the time-average of the Poynting vector, ?S? = (1/T) ?0^T S(z,t) dt ?

Reasoning your answer.

Added by Kathryn N.

Question

Please give Ace some feedback