Please show all work. Will rate positively! Thanks. An electromagnetic wave from

Question

Please show all work. Will rate positively! Thanks.

An electromagnetic wave from a wire antenna travels (from the reader) toward the plane of the paper. At time t = 0.0 s it strikes the paper at normal incidence. At point O and t = 0.0 s, the magnetic field vector has its maximum value, 4.09×10-8 T, pointing in the negative y-direction. The frequency of this wave is 2.11×106 Hz.

What is the x-component of the associated electric field E at time t = 0.0 s? (Use the right-hand rule to determine the direction of E, and hence the sign of the x-component.)

What is the magnitude of the Poynting vector of the wave at time t = 0.0 s?

What is the y component of the magnetic field at point O at time 2.37×10-7 s?

Explanation / Answer

Given,

B = 4.09 x 10^-8 T ; f = 2.11 x 10^6 Hz

1)we know that,

c = E/B

E = cB

E = 3 x 10^8 x 4.09 x 10^-8 = 12.27 V/m

Hence, E = 12.27 V/m

2) Poynting vector will be;

S = EB/u0

S = 12.27 x 4.09 x 10^-8/(4 pi x 10^-7) = 0.4 W/m^2

Hence, S = 0.4 W/m^2

3)t = 2.37 x 10^-7

B = B cos(2 pi f t)

cos(2 pi f t) = cos (2 x 3.14 x 2.11 x 10^6 x 2.37 x 10^-7) = -0.99

B = 4.09 x 10^-8 x -0.99 = -4.05 x 10^-8 T

Hence, B = 4.05 x 10^-8 T

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