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

Answer 1

Answer: (D)

In each case: $\oint \vec{E}\cdot d\vec{A}=\frac{q_{\text{ enclosed}}}{{\epsilon }_0}$
$E\oint dA=\frac{Q}{{\epsilon }_0}$
$E\left(4\pi r^2\right)=\frac{Q}{{\epsilon }_0}$
$E$ $=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$
As charged enclosed within the Gaussian surface is the same, the radius of Gaussian surface is equal. Hence, the magnitude of electric field will be equal.