Find the electric flux density of a material with charge density 16 un...
Answer: c
Explanation: The electric flux density from Maxwell’s equation is given by D = ∫ ρ dv. On substituting ρ = 16 and ∫dv = 1, we get D = 16 units.
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Find the electric flux density of a material with charge density 16 un...
Electric Flux Density
The electric flux density, also known as the electric displacement, is a vector field that describes the electric flux per unit area. It is denoted by the symbol D and is related to the electric field E and the permittivity of the material ε.
Charge Density
The charge density, denoted by ρ, is a scalar quantity that represents the amount of charge per unit volume. It describes the distribution of charge within a given region of space.
Relationship between Electric Flux Density and Charge Density
The electric flux density is directly related to the charge density. Mathematically, the relationship can be expressed as:
D = εE
where D is the electric flux density, ε is the permittivity of the material, and E is the electric field.
Given Information
In the given problem, the charge density is given as 16 units in unit volume.
Solution
To find the electric flux density, we need to determine the electric field E and the permittivity ε.
Since we are not given any information about the electric field E, we cannot directly calculate the electric flux density using the given charge density.
However, we can make some general observations:
1. The electric field E is directly proportional to the charge density ρ.
2. The electric field E is inversely proportional to the permittivity ε.
Therefore, if the charge density is increased, the electric field will also increase. Similarly, if the permittivity is decreased, the electric field will increase.
Since we are not given any information about the permittivity ε, we cannot determine the exact value of the electric flux density.
However, based on the given options, we can make a reasonable assumption that the permittivity ε is constant and equal to 1.
Therefore, the electric flux density D is equal to the charge density ρ.
Given that the charge density is 16 units in unit volume, the electric flux density D is also 16 units.
Therefore, the correct answer is option C: 16.
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