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Answer: c
Explanation: Total flux leaving the entire surface is, ψ = 4πr2D from Gauss law. Ψ =
4π(1/16π2) X 16π = 4.
To calculate the total electric flux (Φ) through the surface of a sphere, you can use Gauss’s law, which states that the total electric flux through a closed surface is equal to the electric flux density (D) multiplied by the surface area of the sphere (A).
1. Calculate the Surface Area of the Sphere (A):
The formula for the surface area of a sphere is:
[
A = 4pi r^2
]
Given the radius ( r = frac{1}{4pi} , text{m} ):
[
A = 4pi left(frac{1}{4pi}right)^2 = 4pi cdot frac{1}{16pi^2} = frac{1}{4pi}
]
2. Calculate the Total Electric Flux (Φ):
The total electric flux is given by:
[
Φ = D cdot A
]
where ( D = 16pi ) (electric flux density). Now substituting the values:
[
Φ = 16pi cdot frac{1}{4pi} = 4
]
So, the total flux is 4 units.