Consider a point charge +Q located outside a closed surface...

Consider a point charge $+Q$ located outside a closed surface such as a sphere bound by the black circle in Figure $16-24$. What is the net electric flux through the closed surface? A. $+\mathrm{Q} \varepsilon 0^{\frac{+Q}{\varepsilon_{0}}}$ B. $-\mathrm{Q} \varepsilon 0^{\frac{-Q}{\varepsilon_{0}}}$ C. 0 D. $+2 \mathrm{Q} \varepsilon 0^{\frac{+2 Q}{\varepsilon_{0}}}$ E. $-2 \mathrm{Q} \varepsilon 0^{\frac{-2 Q}{\varepsilon_{0}}}$

Consider a point charge $+Q$ located outside a closed surface such as a sphere bound by the black circle in Figure $16-24$. What is the net electric flux through the closed surface?
A. $+\mathrm{Q} \varepsilon 0^{\frac{+Q}{\varepsilon_{0}}}$
B. $-\mathrm{Q} \varepsilon 0^{\frac{-Q}{\varepsilon_{0}}}$
C. 0
D. $+2 \mathrm{Q} \varepsilon 0^{\frac{+2 Q}{\varepsilon_{0}}}$
E. $-2 \mathrm{Q} \varepsilon 0^{\frac{-2 Q}{\varepsilon_{0}}}$

Key Concepts

Gauss's Law

Gauss's law is a fundamental principle in electromagnetism that relates the net electric flux through a closed surface to the charge enclosed by that surface. It is mathematically expressed as the flux being equal to the enclosed charge divided by the permittivity of free space. This concept is crucial for solving problems involving electric fields and closed surfaces, as it simplifies the calculation of net flux especially when dealing with symmetric charge distributions.

Electric Flux

Electric flux represents the total amount of electric field passing through a given surface. It quantifies how many electric field lines cross the surface and is a key parameter in applying Gauss's law. Understanding electric flux helps in determining the effect of the field on a surface, particularly when analyzing whether the field contributions cancel due to symmetry or the arrangement of charges.

Enclosed Charge

Enclosed charge refers to the total charge located within a closed surface. In the context of Gauss's law, the net electric flux depends solely on the charge that is enclosed by the surface. Charges located outside the surface do not affect the net flux through the surface, even though they might contribute to the electric field at points on the surface.

Closed Surface

A closed surface is a continuous boundary that completely encloses a volume, with no gaps or openings. In the application of Gauss's law, closed surfaces, such as spheres or cubes, are used to determine the net flux through a boundary, ensuring that only the charge inside the boundary contributes to the net flux calculation.

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