Question

\(\sigma\) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is:

• A. \( \frac{\sigma}{\epsilon_0 R} \)
• B. \( \frac{\sigma}{2\epsilon_0} \)
• C. \( \frac{\sigma}{\epsilon_0} \)
• D. \( \frac{\sigma}{4\epsilon_0} \)

Answer 1

The Correct Option is C

By Gauss's Law:

\[ \oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{in}}}{\varepsilon_0}. \]

For a spherical shell, the electric field \( E \) is constant across the surface area:

\[ E \cdot 4\pi R^2 = \frac{\sigma \cdot 4\pi R^2}{\varepsilon_0}. \]



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

Thus, the electric field at the surface of the spherical shell is:

\[ \boxed{\frac{\sigma}{\varepsilon_0}}. \]