#line charge

Continuous Charge Distribution

An infinite line charge has \( E = 7.2 \times 10^5 \, \text{N/C} \) at 5 cm. What is \( \lambda \)?

**Continuous distribution** uses linear density λ = dq/dl (C/m), surface σ = dq/dA, volume ρ = dq/dV. Field of infinite line with uniform λ is E = 2kλ/r = λ/(2π ε₀ r) radially outward, derived via cylindrical Gaussian surface, showing 1/r dependence. E = (2 k λ/r) . 7.2 × 10⁵ = (2 × 9 × 10⁹ × λ/0.05) . λ = (7.2 × 10⁵ × 0.05/18 × 10⁹) = 2 × 10⁻⁶ C/m . Substituting values gives 2.0 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( \lambda = 1.5 \times 10^{-6} \, \text{C/m} \). What is the electric field at 50 cm?

**Continuous distribution** uses linear density λ = dq/dl (C/m), surface σ = dq/dA, volume ρ = dq/dV. Field of infinite line with uniform λ is E = 2kλ/r = λ/(2π ε₀ r) radially outward, derived via cylindrical Gaussian surface, showing 1/r dependence. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 1.5 × 10⁻⁶/0.5) = 5.4 × 10⁴ N/C . Substituting values gives 5.4 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( E = 6.0 \times 10^5 \, \text{N/C} \) at 3 cm. What is \( \lambda \)?

**Continuous distribution** uses linear density λ = dq/dl (C/m), surface σ = dq/dA, volume ρ = dq/dV. Field of infinite line with uniform λ is E = 2kλ/r = λ/(2π ε₀ r) radially outward, derived via cylindrical Gaussian surface, showing 1/r dependence. E = (2 k λ/r) . 6.0 × 10⁵ = (2 × 9 × 10⁹ × λ/0.03) . λ = (6.0 × 10⁵ × 0.03/18 × 10⁹) = 1 × 10⁻⁶ C/m . Substituting values gives 1.0 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( E = 3.6 \times 10^5 \, \text{N/C} \) at 10 cm. What is \( \lambda \)?

**Line charge concept** extends point charge to infinite wire where symmetry dictates radial field proportional to λ and inversely proportional to distance r. λ = q/L for uniform case, field direction depends on sign of λ, outward for positive. E = (2 k λ/r) . 3.6 × 10⁵ = (2 × 9 × 10⁹ × λ/0.1) . λ = (3.6 × 10⁵ × 0.1/18 × 10⁹) = 2 × 10⁻⁶ C/m . Substituting values gives 2.0 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( \lambda = 5 \times 10^{-7} \, \text{C/m} \). What is the electric field at 10 cm?

**Charge density formulation** allows integration over extended bodies, but highly symmetric cases yield simple expressions. Infinite line gives E ∝ λ/r, unlike point charge 1/r², reflecting different geometry of source. E = (2 k λ/r) . E = (2 × 9 × 10⁹ × 5 × 10⁻⁷/0.1) = 9 × 10⁴ N/C . Substituting values gives 9.0 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency. This aligns with NCERT Class 11 treatment, emphasizing conservation, symmetry and dimensional consistency useful for CBSE

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( \lambda = 9 \times 10^{-7} \, \text{C/m} \). What is the electric field at 30 cm?

**Charge density formulation** allows integration over extended bodies, but highly symmetric cases yield simple expressions. Infinite line gives E ∝ λ/r, unlike point charge 1/r², reflecting different geometry of source. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 9 × 10⁻⁷/0.3) = 5.4 × 10⁴ N/C . Substituting values gives 5.4 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( \lambda = 7 \times 10^{-7} \, \text{C/m} \). What is the electric field at 25 cm?

**Charge density formulation** allows integration over extended bodies, but highly symmetric cases yield simple expressions. Infinite line gives E ∝ λ/r, unlike point charge 1/r², reflecting different geometry of source. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 7 × 10⁻⁷/0.25) = 5.04 × 10⁴ N/C . Substituting values gives 5.04 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has a linear charge density of \( 4 \times 10^{-6} \, \text{C/m} \). What is the electric field

**Charge density formulation** allows integration over extended bodies, but highly symmetric cases yield simple expressions. Infinite line gives E ∝ λ/r, unlike point charge 1/r², reflecting different geometry of source. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 4 × 10⁻⁶/0.08) = 9 × 10⁵ N/C . Substituting values gives 9.0 × 10⁵ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( E = 4.5 \times 10^5 \, \text{N/C} \) at 8 cm. What is \( \lambda \)?

**Line charge concept** extends point charge to infinite wire where symmetry dictates radial field proportional to λ and inversely proportional to distance r. λ = q/L for uniform case, field direction depends on sign of λ, outward for positive. E = (2 k λ/r) . 4.5 × 10⁵ = (2 × 9 × 10⁹ × λ/0.08) . λ = (4.5 × 10⁵ × 0.08/18 × 10⁹) = 2 × 10⁻⁶ C/m . Substituting values gives 2.0 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Continuous Charge Distribution

An infinite line charge has \( \lambda = 1.2 \times 10^{-6} \, \text{C/m} \). What is the electric field at 40 cm?

**Line charge concept** extends point charge to infinite wire where symmetry dictates radial field proportional to λ and inversely proportional to distance r. λ = q/L for uniform case, field direction depends on sign of λ, outward for positive. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 1.2 × 10⁻⁶/0.4) = 5.4 × 10⁴ N/C . Substituting values gives 5.4 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Continuous Charge Distribution

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Electric Charge, Quantization and Conservation

An infinite line charge has \( E = 6.3 \times 10^5 \, \text{N/C} \) at 7 cm. What is \( \lambda \)?

**Fundamental property of charge** includes additivity and quantization, meaning net charge equals algebraic sum of constituents and each is multiple of e. When rod loses charge, electron removal is inferred, and n = q/e gives transferred count. E = (2 k λ/r) . 6.3 × 10⁵ = (2 × 9 × 10⁹ × λ/0.07) . λ = (6.3 × 10⁵ × 0.07/18 × 10⁹) = 2.45 × 10⁻⁶ C/m . Substituting values gives 2.45 × 10⁻⁶ C/m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Charge, Quantization and Conservation

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Electric Charge, Quantization and Conservation

An infinite line charge has \( \lambda = 3 \times 10^{-6} \, \text{C/m} \). What is the electric field at 15 cm?

**Quantization of charge** states observable charge is integer multiple of elementary charge e = 1.6×10⁻¹⁹ C, q = n·e, and total charge is conserved in isolated systems. Loss of electrons produces positive charge, and number of transferred electrons follows n = q/e, linking macroscopic charge measurement to microscopic carriers. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 3 × 10⁻⁶/0.15) = 3.6 × 10⁵ N/C . Substituting values gives 3.6 × 10⁵ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Charge, Quantization and Conservation

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