Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = − 2 at R = 4m and σ = − 3 at R = 5m. Find the flux density at R = 3m.
⚑ Report issue
Found a wrong answer, translation, image or source problem? Send it to editorial review.
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.
Formula / Key Relation
D(2πrL) = σ(2πaL)
D = σa/r
= 5×2/3
= 10/3
Detailed Explanation
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…
Concept & Reasoning
Choose 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 Exam
For concentric sheets, include only charges with radius less than the observation radius.
Important Exam Point
List enclosed sheets before writing Gauss' law.
Related Revision Path
This question sits in the revision path Electromagnetic Fields → Gauss Law → Cylindrical Charge Distribution .
Quick Trick
For concentric sheets, include only charges with radius less than the observation radius.
Common Mistake
Adding charges from the 4 m and 5 m sheets at r=3 m violates the enclosed-charge rule.
Exam Tip
List enclosed sheets before writing Gauss' law.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 144
