#total charge

Continuous Charge Distribution

A conducting sphere of radius 30 cm has a surface charge density of \( 50 \, \mu\text{C/m}^2 \). What is the total charg

**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. Surface area: A = 4 π r² = 4 π (0.3)² = 0.36 π m² . Charge: q = sigma A = 50 × 10⁻⁶ × 0.36 π = 5.654 × 10⁻⁵ C . Substituting values gives 5.65 × 10⁻⁵ 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

A conducting sphere of radius 17 cm has a surface charge density of \( 15 \, \mu\text{C/m}^2 \). What is the total charg

**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. Surface area: A = 4 π r² = 4 π (0.17)² = 0.1156 π m² . Charge: q = sigma A = 15 × 10⁻⁶ × 0.1156 π = 5.45 × 10⁻⁶ C . Substituting values gives 5.45 × 10⁻⁶ 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

A conducting sphere of radius 20 cm has a surface charge density of \( 30 \, \mu\text{C/m}^2 \). What is the total charg

**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. Surface area: A = 4 π r² = 4 π (0.2)² = 0.16 π m² . Charge: q = sigma A = 30 × 10⁻⁶ × 0.16 π = 1.507 × 10⁻⁵ C . Substituting values gives 1.51 × 10⁻⁵ 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

A conducting sphere of radius 23 cm has a surface charge density of \( 35 \, \mu\text{C/m}^2 \). What is the total charg

**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. Surface area: A = 4 π r² = 4 π (0.23)² = 0.2116 π m² . Charge: q = sigma A = 35 × 10⁻⁶ × 0.2116 π = 2.33 × 10⁻⁵ C . Substituting values gives 2.33 × 10⁻⁵ 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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