Question

Which expression for the outside field of a uniformly charged thin spherical shell uses its surface charge density \[\sigma\]?

Options

• \[E = \frac{\sigma r^2}{\varepsilon_0 R^2}\]

• \[E = \frac{\sigma R^2}{\varepsilon_0 r^2}\]

• \[E = \frac{\sigma R}{2\varepsilon_0 r}\]

• \[E = \frac{\sigma}{\varepsilon_0}\]

Answer 1

The shell's total charge can be expressed using its surface charge density and radius. Substitution into the outside-field expression gives \[E = \sigma R^2/(\varepsilon_0 r^2)\].