Question

Figure shows, in cross section, three solid cylinders, each of length $L$ and uniform charge $Q$. Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius. Rank the Gaussian surfaces according to the electric field at any point on the surface, greatest first.

• A. $II\to I\to III$
• B. $I\to II\to III$
• C. All tie
• D. $III\to II\to I$

Answer 1

The correct option is C All tie


Let r be the radius of the Gaussian surface. According to the Gauss law net flux,

$\varphi =\frac{Q_{\text{inside}}}{{\epsilon }_0}$

$\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{q_{\text{enclosed}}}{{\epsilon }_0}$

$E\int dA=\frac{Q}{{\epsilon }_0}\Rightarrow E\left(4\pi r^2\right)=\frac{Q}{{\epsilon }_0}$

$E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$

The charge enclosed within the Gaussian surface is the same and the radius of the Gaussian surface is equal. Hence, the magnitude of the electric field will also be equal.