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A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above?
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A uniform line charge with linear density λ lies along the y-axis. Wha...
Flux Calculation of a Uniform Line Charge on a Spherical Surface
Flux through a closed surface is given by the formula Φ = ∮E⋅dA, where E is the electric field and dA is the area element vector.
Gaussian Surface Selection
In this case, we will choose a spherical Gaussian surface centered at the origin with radius r = R.
Electric Field Calculation
The electric field E due to a line charge is given by E = (λ/2πε₀r) in the radial direction.
Flux Calculation
To calculate the flux through the Gaussian surface, we need to find the total electric field passing through it. Since the electric field is radial, it is perpendicular to the surface at every point.
Therefore, the flux through the spherical surface will be the same as the flux through a flat circular surface with the same radius R. The flux through a flat circular surface due to a line charge is given by Φ = E * 4πR².
Substitute the expression for E into the equation, we get Φ = (λ/2πε₀R) * 4πR² = 2λR/ε₀.
Therefore, the correct answer is Option A: 2Rλ/ε₀.
Flux through a closed surface is given by the formula Φ = ∮E⋅dA, where E is the electric field and dA is the area element vector.
Gaussian Surface Selection
In this case, we will choose a spherical Gaussian surface centered at the origin with radius r = R.
Electric Field Calculation
The electric field E due to a line charge is given by E = (λ/2πε₀r) in the radial direction.
Flux Calculation
To calculate the flux through the Gaussian surface, we need to find the total electric field passing through it. Since the electric field is radial, it is perpendicular to the surface at every point.
Therefore, the flux through the spherical surface will be the same as the flux through a flat circular surface with the same radius R. The flux through a flat circular surface due to a line charge is given by Φ = E * 4πR².
Substitute the expression for E into the equation, we get Φ = (λ/2πε₀R) * 4πR² = 2λR/ε₀.
Therefore, the correct answer is Option A: 2Rλ/ε₀.
Community Answer
A uniform line charge with linear density λ lies along the y-axis. Wha...
I think ans. is A
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A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above?
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A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above?.
A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical surface cantered at the origin with r = R A: 2Rλ/ε0 B: Rλ/ε0 C: λ/ε0 D: none of the above?.
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