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An AM radio station broadcasts isotropically (equally in all directions) with an average power of 3.80 kW. A receiving antenna 75.0 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.

User Cryssie
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1 Answer

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Final answer:

To find the amplitude of the emf induced in the receiving antenna, we can use the formula: Emf = (2 * Pi * f * B * A * N) / c, where f is the frequency of the radio wave, B is the maximum strength of the magnetic field, A is the cross-sectional area of the coil, N is the number of turns in the coil, and c is the speed of light.

Step-by-step explanation:

To calculate the amplitude of the emf induced in the receiving antenna, we can use the formula:

Emf = (2 * Pi * f * B * A * N) / c

Where:
- Emf is the induced electromotive force
- Pi is a mathematical constant approximately equal to 3.1416
- f is the frequency of the radio wave
- B is the maximum strength of the magnetic field
- A is the cross-sectional area of the coil
- N is the number of turns in the coil
- c is the speed of light

Given that the radio frequency is 100 MHz, the maximum strength of the magnetic field is 1.00×10^-12 T, the cross-sectional area of the coil is (Pi * (0.75 m)^2), and the number of turns in the coil is 200, we can substitute these values into the formula to find the answer.

Emf = (2 * Pi * (100 × 10^6) * (1.00×10^-12) * (Pi * (0.75 m)^2) * 200) / 3.00×10^8

Solving this equation will give us the amplitude of the emf induced in the receiving antenna.

User Majeed
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