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The electric flux (Phi) through a surface is given by the equation:
[
Phi = text{Electric flux density} times text{Surface area}
]
Given that the radius of the sphere is (frac{1}{4pi}) meters, we first calculate the surface area (A) of the sphere using the formula for the surface area of a sphere, (A = 4pi r^2), where (r) is the radius of the sphere:
[
A = 4pi left(frac{1}{4pi}right)^2 = 4pi left(frac{1}{16pi^2}right) = frac{1}{4pi}
]
The electric flux density is given as (16pi) units. Therefore, the total electric flux (Phi) is:
[
Phi = text{Electric flux density} times text{Surface area} = 16pi times frac{1}{4pi} = 4
]
So, the total flux is (4) units.
c
Explanation: Total flux leaving the entire surface is, ψ = 4πr2D from Gauss law. Ψ =
4π(1/16π2
) X 16π = 4.