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#line charge

10 public questions tagged with this topic.

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 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 \( \lambda = 6 \times 10^{-6} \, \text{C/m} \). What is the electric field at 12 cm?

**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) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 6 × 10⁻⁶/0.12) = 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 > Electric Charge, Quantization and Conservation

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Electric Charge, Quantization and Conservation

An infinite line charge has \( \lambda = 8 \times 10^{-7} \, \text{C/m} \). What is the electric field at 20 cm?

**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) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 8 × 10⁻⁷/0.2) = 7.2 × 10⁴ N/C . Substituting values gives 7.2 × 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 > Electric Charge, Quantization and Conservation

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Continuous Charge Distribution

An infinite line charge has a linear charge density \( \lambda = 2 \times 10^{-6} \, \text{C/m} \). What is the electric

**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 = (λ/2 π ε₀ r) , k = (1/4 π ε₀) = 9 × 10⁹ , so (1/ε₀) = 4 π × 9 × 10⁹ . E = (2 × 10⁻⁶/2 π × 8.854 × 10⁻¹² × 0.05) = 7.19 × 10⁵ N/C . Or, E = (2kλ/r) = (2 × 9 × 10⁹ × 2 × 10⁻⁶/0.05) = 7.2 × 10⁵ N/C . Substituting

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 \( E = 4.5 \times 10^5 \, \text{N/C} \) at 4 cm. What is \( \lambda \)?

**Charge conservation and quantization** govern rubbing processes where electrons transfer without creation. Total charge before and after remains equal, and any measured charge corresponds to n = q/e electrons, allowing counting of carriers from coulomb value. E = (2 k λ/r) . 4.5 × 10⁵ = (2 × 9 × 10⁹ × λ/0.04) . λ = (4.5 × 10⁵ × 0.04/18 × 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 > Electric Charge, Quantization and Conservation

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Electric Charge, Quantization and Conservation

An infinite line charge produces \( E = 3.6 \times 10^5 \, \text{N/C} \) at 5 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) . 3.6 × 10⁵ = (2 × 9 × 10⁹ × λ/0.05) . λ = (3.6 × 10⁵ × 0.05/18 × 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 > Electric Charge, Quantization and Conservation

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