An AM radio station broadcasts isotropically (equally in all directions) with an average power of 3.40 kW. A receiving antenna 60.0 cm long is at a location 4.00 mi from the transmitter. Compute the amplitude of the emf that is induced by this signal between the ends of the receiving antenna.

To solve the problem we will apply the concepts related to the Intensity as a function of the power and the area, as well as the electric field as a function of the current, the speed of light and the permeability in free space, as shown below.

The intensity of the wave at the receiver is

The amplitude of electric field at the receiver is

The amplitude of induced emf by this signal between the ends of the receiving antenna is

Here,

I = Current

= Permeability at free space

c = Light speed

d = Distance

Replacing,

Thus, the amplitude of induced emf by this signal between the ends of the receiving antenna is 0.0543V

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