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An infinitely long hollow cylinder of radius R carrying a surface charge density σ is rotated about its cylindrical axis with a constant angular speed ω. The magnitude of the surface current is
- a)2σRω
- b)σR2ω
- c)2πσRω
- d)πσRω
Correct answer is option 'B'. Can you explain this answer?
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An infinitely long hollow cylinder of radiusRcarrying a surface charge...
Applying Ampere’s law
The correct answer is: σR2ω
Most Upvoted Answer
An infinitely long hollow cylinder of radiusRcarrying a surface charge...
To find the electric field inside the hollow cylinder, we'll use Gauss's law. Gauss's law states that the electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of free space (ε0).
In this case, we'll consider a Gaussian cylinder of radius r inside the hollow cylinder, with length L. The Gaussian cylinder is chosen such that it is coaxial with the hollow cylinder. Since the hollow cylinder is infinitely long, we can ignore any end effects.
The only charge enclosed by the Gaussian cylinder is the charge on the inner surface of the hollow cylinder. The charge per unit length on the inner surface of the hollow cylinder can be calculated by multiplying the surface charge density (σ) by the circumference of the inner surface of the hollow cylinder (2πR). Therefore, the total charge enclosed is σ(2πR)L.
Using Gauss's law, we can write:
Electric flux = (Total charge enclosed) / (ε0)
The electric flux through the Gaussian cylinder is given by E * (2πrL), where E is the electric field inside the hollow cylinder. Therefore, we have:
E * (2πrL) = σ(2πR)L / ε0
Simplifying, we find:
E = σR / (ε0r)
Thus, the electric field inside the hollow cylinder is given by E = σR / (ε0r).
In this case, we'll consider a Gaussian cylinder of radius r inside the hollow cylinder, with length L. The Gaussian cylinder is chosen such that it is coaxial with the hollow cylinder. Since the hollow cylinder is infinitely long, we can ignore any end effects.
The only charge enclosed by the Gaussian cylinder is the charge on the inner surface of the hollow cylinder. The charge per unit length on the inner surface of the hollow cylinder can be calculated by multiplying the surface charge density (σ) by the circumference of the inner surface of the hollow cylinder (2πR). Therefore, the total charge enclosed is σ(2πR)L.
Using Gauss's law, we can write:
Electric flux = (Total charge enclosed) / (ε0)
The electric flux through the Gaussian cylinder is given by E * (2πrL), where E is the electric field inside the hollow cylinder. Therefore, we have:
E * (2πrL) = σ(2πR)L / ε0
Simplifying, we find:
E = σR / (ε0r)
Thus, the electric field inside the hollow cylinder is given by E = σR / (ε0r).
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An infinitely long hollow cylinder of radiusRcarrying a surface charge...
Applying Ampere’s law
The correct answer is: σR2ω
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An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer?
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An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer?.
An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An infinitely long hollow cylinder of radiusRcarrying a surface charge densityσis rotated about its cylindrical axis with a constant angular speedω.The magnitude of the surface current isa)2σRωb)σR2ωc)2πσRωd)πσRωCorrect answer is option 'B'. Can you explain this answer?.
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