#enclosed charge

Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 9.04 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Gauss's theorem** states total flux through closed surface equals enclosed charge divided by free-space permittivity, Φ_total = q_enc/ε₀, ε₀ = 8.854×10⁻¹² C²/(N·m²). Result independent of shape or size, depends only on net enclosed charge, enabling charge determination from flux. Φ = (q/ε₀) . q = Φ ε₀ = 9.04 × 10⁵ × 8.854 × 10⁻¹² = 8 × 10⁻⁶ C = 8 μC . Substituting values gives 8.0 μC, 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 > Gauss's Theorem and Total Flux

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Gauss's Theorem and Total Flux

A net flux of \( 9.04 \times 10^4 \, \text{Nm}^2/\text{C} \) passes through a closed surface. What is the charge enclose

**Gauss's theorem** states total flux through closed surface equals enclosed charge divided by free-space permittivity, Φ_total = q_enc/ε₀, ε₀ = 8.854×10⁻¹² C²/(N·m²). Result independent of shape or size, depends only on net enclosed charge, enabling charge determination from flux. Φ = (q/ε₀) . q = Φ ε₀ = 9.04 × 10⁴ × 8.854 × 10⁻¹² = 8 × 10⁻⁷ C = 0.8 μC . Substituting values gives 0.8 μC, 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 > Gauss's Theorem and Total Flux

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Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 7.91 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Gauss's law** Φ = ∮ E·dA = q_enc/ε₀ is fundamental relation between flux and enclosed charge. For charge at centre of cube, total flux = q/ε₀ distributes equally over six faces, each receiving Φ/6, but total remains q/ε₀ irrespective of cube edge. Φ = (q/ε₀) . q = Φ ε₀ = 7.91 × 10⁵ × 8.854 × 10⁻¹² = 7 × 10⁻⁶ C = 7 μC . Substituting values gives 7.0 μC, 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 > Gauss's Theorem and Total Flux

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Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 3.39 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Closed-surface flux** depends solely on net charge inside, not external charges. This principle allows flux calculation without detailed field integration and forms cornerstone for symmetric charge distributions. Φ = (q/ε₀) . q = Φ ε₀ = 3.39 × 10⁵ × 8.854 × 10⁻¹² = 3 × 10⁻⁶ C = 3 μC . Substituting values gives 3.0 μC, 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, NEET and CUET.

Ref: NCERT > Physics Book > Electric Charges and Fields > Gauss's Theorem and Total Flux

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Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 2.26 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Gauss's theorem** states total flux through closed surface equals enclosed charge divided by free-space permittivity, Φ_total = q_enc/ε₀, ε₀ = 8.854×10⁻¹² C²/(N·m²). Result independent of shape or size, depends only on net enclosed charge, enabling charge determination from flux. Φ = (q/ε₀) . q = Φ ε₀ = 2.26 × 10⁵ × 8.854 × 10⁻¹² = 2 × 10⁻⁶ C = 2 μC . Substituting values gives 2.0 μC, 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 > Gauss's Theorem and Total Flux

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Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 4.52 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Closed-surface flux** depends solely on net charge inside, not external charges. This principle allows flux calculation without detailed field integration and forms cornerstone for symmetric charge distributions. Φ = (q/ε₀) . q = Φ ε₀ = 4.52 × 10⁵ × 8.854 × 10⁻¹² = 4 × 10⁻⁶ C = 4 μC . Substituting values gives 4.0 μC, 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, NEET and CUET.

Ref: NCERT > Physics Book > Electric Charges and Fields > Gauss's Theorem and Total Flux

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Electric Flux

A charge of \( 5 \, \mu\text{C} \) is enclosed in a cube of edge 30 cm. What is the flux through one face?

**Electric flux** through surface measures field lines crossing it, Φ = E·A = E A cosθ for uniform field, unit N·m²/C. For circular area in xy-plane with field along z, θ = 0°, cosθ = 1, so Φ = E·πR² directly, maximum when field normal to surface. Total flux: Φ = (q/ε₀) = (5 × 10⁻⁶/8.854 × 10⁻¹²) = 5.65 × 10⁵ N·m²/C . Flux per face (6 faces): Φfₐcₑ = (5.65 × 10⁵/6) = 9.42 × 10⁴ N·m²/C . Substituting values gives 9.42 × 10⁴ N·m²/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 Flux

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Electric Flux

A charge of \( 3 \, \mu\text{C} \) is enclosed in a cube of edge 15 cm. What is the flux through one face?

**Electric flux** through surface measures field lines crossing it, Φ = E·A = E A cosθ for uniform field, unit N·m²/C. For circular area in xy-plane with field along z, θ = 0°, cosθ = 1, so Φ = E·πR² directly, maximum when field normal to surface. Total flux: Φ = (q/ε₀) = (3 × 10⁻⁶/8.854 × 10⁻¹²) = 3.39 × 10⁵ N·m²/C . Flux per face (6 faces): Φfₐcₑ = (3.39 × 10⁵/6) = 5.65 × 10⁴ N·m²/C . Substituting values gives 5.65 × 10⁴ N·m²/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 Flux

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Gauss's Theorem and Total Flux

A closed surface has a net flux of \( 5.65 \times 10^5 \, \text{Nm}^2/\text{C} \). What is the charge enclosed?

**Closed-surface flux** depends solely on net charge inside, not external charges. This principle allows flux calculation without detailed field integration and forms cornerstone for symmetric charge distributions. Φ = (q/ε₀) . q = Φ ε₀ = 5.65 × 10⁵ × 8.854 × 10⁻¹² = 5 × 10⁻⁶ C = 5 μC . Substituting values gives 5.0 μC, 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, NEET and CUET.

Ref: NCERT > Physics Book > Electric Charges and Fields > Gauss's Theorem and Total Flux

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