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To find the flux density (electric flux density, ( mathbf{D} )) of a line charge, we can use Gauss’s law for electricity. The formula for ( mathbf{D} ) due to a line charge is given by:
[
mathbf{D} = frac{lambda}{2 pi r}
]
where:
– ( lambda ) is the linear charge density (charge per unit length),
– ( r ) is the distance from the line charge.
Given:
– Charge density (which should be interpreted as linear charge density) ( lambda = 3.14 , text{units} ),
– Radius ( r = 2 , text{m} ).
Now, plug the values into the formula:
[
mathbf{D} = frac{3.14}{2 pi (2)}
]
Calculating this:
[
mathbf{D} = frac{3.14}{4 pi} approx frac{3.14}{12.5664} approx 0.25 , text{units}
]
Therefore, the flux density of the line charge is approximately ( 0.25 , text{units} ).
Answer: d
Explanation: The electric field of a line charge is given by, E = λ/(2περ), where ρ is the
radius of cylinder, which is the Gaussian surface and λ is the charge density. The
density D = εE = λ/(2πρ) = 3.14/(2π X 2) = 1/4 = 0.25.