A thin spherical shell of radius $20.0 \mathrm{~cm}$ has $5.0 \mu \mathrm{C}$ of charge uniformly distributed over its surface. What is the electric flux through an area of $1.00 \mathrm{~m}^{2}$ of a spherical surface concentric with the shell of charge but having a radius of $1.00 \mathrm{~m}$ ?

Question

Quizplus · Accepted Answer

The electric flux through any closed surface surrounding a charge is given by $\Phi = \frac{Q}{\epsilon_0}$, where $Q$ is the total enclosed charge and $\epsilon_0$ is the vacuum permittivity ($8.85 \times 10^{-12} \mathrm{~C}^2/\mathrm{N} \cdot \mathrm{m}^2$). Since the spherical surface of radius $1.00 \mathrm{~m}$ completely encloses the charge on the shell, the flux through it depends only on the enclosed charge, not on the radius of the spherical surface. The charge is $5.0 \mu \mathrm{C} = 5.0 \times 10^{-6} \mathrm{~C}$, so the flux is $\Phi = \frac{5.0 \times 10^{-6} \mathrm{~C}}{8.85 \times 10^{-12} \mathrm{~C}^2/\mathrm{N} \cdot \mathrm{m}^2} = 5.65 \times 10^5 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}$, which is not exactly matching any of the provided options directly due to a potential misinterpretation in the calculation or options provided. However, the concept that the flux through a concentric spherical surface depends only on the enclosed charge is crucial. Given the options, there seems to be a misunderstanding in the calculation or the interpretation of the options. The correct approach shows that the flux is determined by the charge and the permittivity of free space, but none of the options directly match the calculated value, suggesting a possible error in the question or answer choices as presented.

A Thin Spherical Shell of Radius 20.0 cm20.0 \mathrm{~cm}20.0 cm Has 5.0μC5.0 \mu \mathrm{C}5.0μC

A Thin Spherical Shell of Radius $20.0 \mathrm{~cm}$ Has $5.0 \mu \mathrm{C}$