Using Gauss's Law

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AP Physics C: Electricity and Magnetism › Using Gauss's Law

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A charge, , is enclosed by two spherical surfaces of radii and , with . The cross-sectional side view is shown.

Ps0_gauss

Which is the correct relationship between the electric flux passing through the two spherical surfaces around the point charge?

$\phi _{1}=\phi _{2}$

$\phi _{1}<\phi _{2}$

$\phi _{1}>\phi _{2}$

$\phi _{1}=\phi _{2}=0$

Explanation

Electric flux is given by either side of the equation of Gauss's Law:

$\phi _{e} = \oint \vec{E}\cdot d\vec{A}=\frac{Q}{\varepsilon_{o} }$

Since the charge is the same for both spherical surfaces, even though these surfaces are of different radii, the amounts of electric flux passing through each surface is the same.

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