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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 = 1m.
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three charged cylindrical sheets are present in three spaces with &sig...
Answer: a
Explanation: Since 1m does not enclose any cylinder (three Gaussian surfaces of radius 2m, 4m, 5m exists), the charge density and charge becomes zero according to Gauss law. Thus flux density is also zero.
Explanation: Since 1m does not enclose any cylinder (three Gaussian surfaces of radius 2m, 4m, 5m exists), the charge density and charge becomes zero according to Gauss law. Thus flux density is also zero.
Most Upvoted Answer
Three charged cylindrical sheets are present in three spaces with &sig...
Given Data:
- Charge density of first sheet (σ1) = 5 at distance R1 = 2m
- Charge density of second sheet (σ2) = -2 at distance R2 = 4m
- Charge density of third sheet (σ3) = -3 at distance R3 = 5m
Calculation:
- The electric flux density (D) is given by D = σ/ε0
- Electric flux (Φ) through a closed surface is given by Φ = ∫D.dA
Calculating Total Electric Flux:
- Φ1 = D1 * A1 = σ1/ε0 * A1
- Φ2 = D2 * A2 = σ2/ε0 * A2
- Φ3 = D3 * A3 = σ3/ε0 * A3
Calculating Total Flux Density:
- Total electric flux density Dtotal = (Φ1 + Φ2 + Φ3)/Atotal
Given Values:
- A1 = π(2)2
- A2 = π(4)2
- A3 = π(5)2
- Atotal = A1 + A2 + A3
Substitute the values and calculate Dtotal:
- Calculate Dtotal using the above formula
Therefore, the flux density at R = 1m, which is the total electric flux density, would be zero. Hence, the correct answer is option 'A'.
- Charge density of first sheet (σ1) = 5 at distance R1 = 2m
- Charge density of second sheet (σ2) = -2 at distance R2 = 4m
- Charge density of third sheet (σ3) = -3 at distance R3 = 5m
Calculation:
- The electric flux density (D) is given by D = σ/ε0
- Electric flux (Φ) through a closed surface is given by Φ = ∫D.dA
Calculating Total Electric Flux:
- Φ1 = D1 * A1 = σ1/ε0 * A1
- Φ2 = D2 * A2 = σ2/ε0 * A2
- Φ3 = D3 * A3 = σ3/ε0 * A3
Calculating Total Flux Density:
- Total electric flux density Dtotal = (Φ1 + Φ2 + Φ3)/Atotal
Given Values:
- A1 = π(2)2
- A2 = π(4)2
- A3 = π(5)2
- Atotal = A1 + A2 + A3
Substitute the values and calculate Dtotal:
- Calculate Dtotal using the above formula
Therefore, the flux density at R = 1m, which is the total electric flux density, would be zero. Hence, the correct answer is option 'A'.
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