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R = 2m पर σ = 5, R = 4m पर σ = − 2 और R = 5m पर σ = − 3 के साथ तीन चार्ज बेलनाकार शीट तीन स्थानों में मौजूद हैं। R = 3m पर फ्लक्स घनत्व ज्ञात कीजिए।

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उत्तर और व्याख्या
सही उत्तरB. 10/3

त्वरित व्याख्या

At r = 3 m only the cylindrical sheet at r = 2 m is enclosed; the sheets at 4 m and 5 m lie outside. Gauss' law gives D(r) = σa/r = 5×2/3 = 10/3 in the radial direction.

फॉर्मूला / मुख्य संबंध

D(2πrL) = σ(2πaL)
D = σa/r
= 5×2/3
= 10/3

विस्तृत व्याख्या

Concept & ReasoningChoose a coaxial Gaussian cylinder of radius r=3 m and length L. The enclosed charge is σ(2πaL) from the sheet at a=2 m. The outer charged sheets do not contribute to enclosed charge at this Gaussian radius. By symmetry D is radial and constant on the cylindrical Gaussian surface, so D(2πrL)=σ(2πaL), yielding D=σa/r=10/3. This is a direct application of Gauss' law for an infinite cylindrical sheet.How to Solve It in the ExamFor concentric sheets, include only charges with radius less than the observation radius.Important Exam PointList enclosed sheets before writing Gauss' law.Related Revision PathThis question sits in the…

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