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NEET PHYSICSELECTRIC CHARGES AND FIELDSEasy

Question

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

A

2\pi R²E

B

\pi R²/E

C

(\pi R² - \pi R)/E

D

Zero

Step-by-Step Solution

The cylinder consists of three surfaces: two flat circular faces (caps) and one curved surface.

  1. Curved Surface: The area vector is perpendicular to the surface (radially outward), while the electric field is parallel to the axis. The angle between them is 90∘90^\circ. Flux Φcurved=∫EdAcos⁡90∘=0\Phi_{curved} = \int E dA \cos 90^\circ = 0.
  2. Circular Faces: The area vectors for the two faces point outward in opposite directions (parallel and anti-parallel to the field).
  • For the face where the field enters, θ=180∘\theta = 180^\circ, so Φin=E(πR2)cos⁡180∘=−πR2E\Phi_{in} = E(\pi R^2) \cos 180^\circ = -\pi R^2 E.
  • For the face where the field leaves, θ=0∘\theta = 0^\circ, so Φout=E(πR2)cos⁡0∘=+πR2E\Phi_{out} = E(\pi R^2) \cos 0^\circ = +\pi R^2 E.
  1. Total Flux: The net flux is the sum of fluxes through all surfaces: Φtotal=−πR2E+πR2E+0=0\Phi_{total} = -\pi R^2 E + \pi R^2 E + 0 = 0.

Alternatively, according to Gauss's Law, the net flux through a closed surface is zero if there is no charge enclosed within it (qenclosed=0q_{enclosed} = 0). Since the cylinder is merely placed in an external field and encloses no charge, the total flux is zero .

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ELECTRIC CHARGES AND FIELDS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSELECTRIC CHARGES AND FIELDScylinderradiuslengthplaceduniform

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