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Radio station WCCO in Minneapolis broadcasts at a frequency of 8.30×105Hz . At a point some distance from the transmitter, the magnetic-field amplitude of the electromagnetic wave from WCCO is 4.26×10−11 T .

Find the wavelength.
Find the wave number.
Calculate the angular frequency.
Calculate the electric-field amplitude.

User Mladzo
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1 Answer

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Final answer:

The wavelength is 360.48 meters. The wave number is 0.0174 rad/m. The angular frequency is 5.21×10^6 rad/s. The electric-field amplitude is 1.28 V/m.

Step-by-step explanation:

To find the wavelength, we can use the formula: wavelength = speed/frequency. For this question, the frequency of the radio station is given as 8.30×10^5 Hz. The speed of light is the speed at which electromagnetic waves travel, which is approximately 3×10^8 m/s. Substituting these values into the formula, we get: wavelength = (3×10^8 m/s)/(8.30×10^5 Hz) = 360.48 meters.

To find the wave number, we can use the formula: wave number = 2π/wavelength.

Substituting the value we found for wavelength, we get: wave number = 2π/(360.48 meters) = 0.0174 rad/m.

To calculate the angular frequency, we can use the formula: angular frequency = 2π × frequency.

Substituting the given frequency, we get: angular frequency = 2π × (8.30×10^5 Hz)

= 5.21×10^6 rad/s.

To calculate the electric-field amplitude, we can use the formula: electric-field amplitude = magnetic-field amplitude × speed. Substituting the given magnetic-field amplitude and the speed of light, we get: electric-field amplitude = (4.26×10^-11 T) × (3×10^8 m/s) = 1.28 V/m.

User Jignesh Sutar
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