Question:
A cylinder of radius $r$ and length $\ell$ is placed in a uniform electric field $E$ parallel to its axis. The total flux over curved surface area is
A cylinder of radius $r$ and length $\ell$ is placed in a uniform electric field $E$ parallel to its axis. The total flux over curved surface area is
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If field is parallel to surface → flux = 0.
Updated On: May 2, 2026
- $2\pi r \ell E$
- $\frac{2\pi}{\ell} E$
- $2\pi r \ell E$
- $\frac{E}{2\pi r \ell}$
- zero
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The Correct Option is
Solution and Explanation
Concept:
Electric flux:
\[
\Phi = \vec{E} \cdot \vec{A} = EA \cos\theta
\]
Step 1: Field direction:
• Field is parallel to cylinder axis
• Curved surface area is perpendicular to radial direction
Step 2: Angle: \[ \theta = 90^\circ \] \[ \cos 90^\circ = 0 \]
Step 3: Flux: \[ \Phi = EA \cos 90^\circ = 0 \] Final Answer: Zero
Step 1: Field direction:
• Field is parallel to cylinder axis
• Curved surface area is perpendicular to radial direction
Step 2: Angle: \[ \theta = 90^\circ \] \[ \cos 90^\circ = 0 \]
Step 3: Flux: \[ \Phi = EA \cos 90^\circ = 0 \] Final Answer: Zero
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