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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 properties of the medium. In this case, the dielectric medium has a relative permittivity of 9, which means it can support electric fields 9 times stronger than that in free space.
Propagation Velocity of Electromagnetic Wave:
The velocity of propagation of an electromagnetic wave in a medium is given by the equation:
v = c / √(μrεr)
where v is the velocity of propagation, c is the speed of light in vacuum, μr is the relative permeability of the medium, and εr is the relative permittivity of the medium.
In this equation, the relative permeability of the medium is not given, so we assume it to be 1 (as it is for most dielectric materials). Therefore, the equation simplifies to:
v = c / √εr
Effect of Relative Permittivity on Velocity:
The relative permittivity of a medium indicates how much the medium can store electric charge compared to vacuum. A higher relative permittivity means that the medium can store more electric charge, leading to a slower propagation of electromagnetic waves.
In this case, the relative permittivity of the dielectric medium is 9. Therefore, the velocity of propagation in the medium is given by:
v = c / √9
Simplifying the equation, we get:
v = c / 3
This means that the velocity of propagation in the dielectric medium is reduced by a factor of 1/3 compared to its velocity in free space.
Conclusion:
Therefore, the correct answer is option 'D' - the velocity of propagation in the dielectric medium is reduced by a factor of 1/3 compared to free space.
When an electromagnetic wave travels through a dielectric medium, its velocity is affected by the properties of the medium. In this case, the dielectric medium has a relative permittivity of 9, which means it can support electric fields 9 times stronger than that in free space.
Propagation Velocity of Electromagnetic Wave:
The velocity of propagation of an electromagnetic wave in a medium is given by the equation:
v = c / √(μrεr)
where v is the velocity of propagation, c is the speed of light in vacuum, μr is the relative permeability of the medium, and εr is the relative permittivity of the medium.
In this equation, the relative permeability of the medium is not given, so we assume it to be 1 (as it is for most dielectric materials). Therefore, the equation simplifies to:
v = c / √εr
Effect of Relative Permittivity on Velocity:
The relative permittivity of a medium indicates how much the medium can store electric charge compared to vacuum. A higher relative permittivity means that the medium can store more electric charge, leading to a slower propagation of electromagnetic waves.
In this case, the relative permittivity of the dielectric medium is 9. Therefore, the velocity of propagation in the medium is given by:
v = c / √9
Simplifying the equation, we get:
v = c / 3
This means that the velocity of propagation in the dielectric medium is reduced by a factor of 1/3 compared to its velocity in free space.
Conclusion:
Therefore, the correct answer is option 'D' - the velocity of propagation in the dielectric medium is reduced by a factor of 1/3 compared to free space.
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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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