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Guys I wanna know what book is this question is from (electromagnetics)
When an electric oscillator is connected an antenna a uniform plane wave is produced in free space, the wavelength is found to be 40cm. when the same signal is produced in a certain non magnetic material, the wavelength is found to be 25 cm. calculate: The frequency of the oscillator (f). b) The relative permittivity the dielectric material?
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Guys I wanna know what book is this question is from (electromagnetics...
Book: Electromagnetics

Question:
When an electric oscillator is connected to an antenna, a uniform plane wave is produced in free space. The wavelength is found to be 40cm. When the same signal is produced in a certain non-magnetic material, the wavelength is found to be 25 cm. Calculate:
a) The frequency of the oscillator (f).
b) The relative permittivity of the dielectric material.

Solution:

a) Calculation of Frequency (f):
The speed of light in free space, c, is given by the formula:
c = λf
Where:
c = speed of light = 3 x 10^8 meters per second (m/s)
λ = wavelength
f = frequency

In the given problem, the wavelength in free space is 40 cm. Converting it to meters:
λ = 40 cm = 0.4 m

Using the formula, we can rearrange it to solve for frequency:
f = c / λ
f = (3 x 10^8 m/s) / (0.4 m)
f = 7.5 x 10^8 Hz

Therefore, the frequency of the oscillator is 7.5 x 10^8 Hz.

b) Calculation of Relative Permittivity (εr):
The relationship between the wavelength in a material and the wavelength in free space is given by:
λ = λ0 / √εr
Where:
λ = wavelength in the material
λ0 = wavelength in free space
εr = relative permittivity of the material

In the given problem, the wavelength in the material is 25 cm. Converting it to meters:
λ = 25 cm = 0.25 m

We can rearrange the formula to solve for the relative permittivity:
εr = (λ0 / λ)^2
εr = (0.4 m / 0.25 m)^2
εr = 2.56

Therefore, the relative permittivity of the dielectric material is 2.56.

Explanation:
- When an electric oscillator is connected to an antenna, it produces a uniform plane wave in free space.
- The wavelength in free space, denoted as λ0, is the distance between two consecutive peaks or troughs of the wave.
- The frequency of the oscillator, denoted as f, represents the number of complete oscillations the oscillator makes per second.
- The relationship between the wavelength and frequency is given by the formula c = λf, where c is the speed of light in free space.
- By rearranging the formula, we can solve for the frequency f = c / λ.
- In the given problem, the wavelength in free space is 40 cm, which is converted to meters as 0.4 m. Substituting the values, we find the frequency to be 7.5 x 10^8 Hz.
- When the same signal is produced in a certain non-magnetic material, the wavelength changes due to the interaction between the wave and the material
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Guys I wanna know what book is this question is from (electromagnetics)When an electric oscillator is connected an antenna a uniform plane wave is produced in free space, the wavelength is found to be 40cm. when the same signal is produced in a certain non magnetic material, the wavelength is found to be 25 cm. calculate: The frequency of the oscillator (f). b) The relative permittivity the dielectric material?
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