Question

You have decided to increase the detection range of your iphone14 with a high- gain, directional parabolic dish antenna to be able to access more distant cell towers (somewhat more difficult to get into your pocket or purse, however). A 3m-diameter parabolic dish is readily available commercially, and the desired sinusoidal radio signal specification is for Emax = 0.10 μV/m. Assume the antenna absorbs all the radiation that is captured by the dish (100% efficiency):

a. What is the amplitude of the magnetic field in this signal?

b.What is the intensity, I, of the radiation received by the antenna?

c.What is the power received by the antenna?

Answer 1

(a)

E = cB

where c is speed of light

so,

B = E / c

B = 0.10e-6 / 3e8

B = 3.33e-16 T

_______________________

(b)

I = 1/2 * _o * c * E_max²

I = 1/2 * 8.85e-12 * 3e8 * 0.10e-6²

I = 1.32e-17 W/m²

____________________

(c)

Power = I * A ( A = pi * r² where r is radius)

Power = 1.32e-17 * pi * 1.5²

Power = 9.3e-17 W