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A plane electromagnetic wave travels in dielectric medium of relative permittivity 9. Relative to free space, the velocity of propagation in the dielectric is
- a)increased by a factor of 9
- b)increased by a factor of 3
- c)unchanged
- d)reduced by a factor of 1/3
Correct answer is option 'D'. Can you explain this answer?
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Explanation:
When an electromagnetic wave travels through a dielectric medium, its velocity is affected by the relative permittivity (εr) of the medium. The relative permittivity is a measure of how much the electric field within the dielectric is reduced compared to the electric field in free space.
Velocity of propagation:
The velocity of propagation of an electromagnetic wave can be calculated using the formula:
v = c / √(εr)
Where:
v is the velocity of propagation in the dielectric medium,
c is the speed of light in free space (approximately 3x10^8 m/s),
εr is the relative permittivity of the dielectric medium.
Effect of relative permittivity on velocity:
Comparing the formula for velocity of propagation in the dielectric medium to the speed of light in free space, we can see that the velocity is inversely proportional to the square root of the relative permittivity.
Therefore, if the relative permittivity increases, the velocity of propagation in the dielectric medium decreases.
If the relative permittivity decreases, the velocity of propagation in the dielectric medium increases.
Given information:
In the given question, the relative permittivity (εr) of the dielectric medium is given as 9.
Answer:
Therefore, the velocity of propagation in the dielectric medium is reduced by a factor of 1/√9 = 1/3 compared to free space.
Hence, the correct answer is option D, the velocity is reduced by a factor of 1/3.
When an electromagnetic wave travels through a dielectric medium, its velocity is affected by the relative permittivity (εr) of the medium. The relative permittivity is a measure of how much the electric field within the dielectric is reduced compared to the electric field in free space.
Velocity of propagation:
The velocity of propagation of an electromagnetic wave can be calculated using the formula:
v = c / √(εr)
Where:
v is the velocity of propagation in the dielectric medium,
c is the speed of light in free space (approximately 3x10^8 m/s),
εr is the relative permittivity of the dielectric medium.
Effect of relative permittivity on velocity:
Comparing the formula for velocity of propagation in the dielectric medium to the speed of light in free space, we can see that the velocity is inversely proportional to the square root of the relative permittivity.
Therefore, if the relative permittivity increases, the velocity of propagation in the dielectric medium decreases.
If the relative permittivity decreases, the velocity of propagation in the dielectric medium increases.
Given information:
In the given question, the relative permittivity (εr) of the dielectric medium is given as 9.
Answer:
Therefore, the velocity of propagation in the dielectric medium is reduced by a factor of 1/√9 = 1/3 compared to free space.
Hence, the correct answer is option D, the velocity is reduced by a factor of 1/3.
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A plane electromagnetic wave travels in dielectric medium of relative permittivity 9. Relative to free space, the velocity of propagation in the dielectric isa)increased by a factor of 9b)increased by a factor of 3c)unchangedd)reduced by a factor of 1/3Correct answer is option 'D'. Can you explain this answer?
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