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#electric field

81 public questions tagged with this topic.

Continuous Charge Distribution

A conducting sphere of radius 26 cm has a surface charge density of \( 45 \, \mu\text{C/m}^2 \). What is the electric fi

**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. For a conductor: E = (sigma/ε₀) . E = (45 × 10⁻⁶/8.854 × 10⁻¹²) = 5.08 × 10⁶ N/C . Substituting values gives 5.08 × 10⁶ 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 \( \lambda = 1.2 \times 10^{-6} \, \text{C/m} \). 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

A conducting sphere of radius 27 cm has an electric field of \( 6 \times 10^3 \, \text{N/C} \) at 54 cm from its center.

**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 = (k q/r²) . 6 × 10³ = 9 × 10⁹ × (q/(0.54)²) . q = (6 × 10³ × 0.2916/9 × 10⁹) = 1.944 × 10⁻⁷ C . Substituting values gives 1.944 × 10⁻⁷ 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

A point charge \( -9 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 6 m along the x

**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 = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 9 × 10⁻⁶ C , r = 6 m . E = 9 × 10⁹ × (9 × 10⁻⁶/(6)²) = 9 × 10⁹ × (9 × 10⁻⁶/36) = 2.25 × 10³ N/C . Substituting values gives 2.25 × 10³ 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 \( E = 6.3 \times 10^5 \, \text{N/C} \) 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

A point charge \( 10 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 5 m along the z

**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 = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 10 × 10⁻⁶ C , r = 5 m . E = 9 × 10⁹ × (10 × 10⁻⁶/(5)²) = 9 × 10⁹ × (10 × 10⁻⁶/25) = 3.6 × 10³ N/C . Substituting values gives 3.6 × 10³ 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

Two charges \( +2 \, \mu\text{C} \) and \( +3 \, \mu\text{C} \) are 10 cm apart. What is the electric field at a point 5

**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. Distance from +3 μC = 5 cm. E₁ = 9 × 10⁹ × (2 × 10⁻⁶/(0.05)²) = 7.2 × 10⁶ N/C (away). E₂ = 9 × 10⁹ × (3 × 10⁻⁶/(0.05)²) = 1.08 × 10⁷ N/C (towards). Net E = 1.08 × 10⁷ - 7.2 × 10⁶ = 3.6 × 10⁶ N/C (towards +3 μC ). Substituting values gives 3.6 × 10⁶ N/C, which matches expected magnitude for this

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

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Electric Charge, Quantization and Conservation

A point charge \( -6 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 3 m along the y

**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 = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 6 × 10⁻⁶ C , r = 3 m . E = 9 × 10⁹ × (6 × 10⁻⁶/(3)²) = 9 × 10⁹ × (6 × 10⁻⁶/9) = 6 × 10³ N/C . Substituting values gives 6 × 10³ N/C, which matches

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

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Field Due to Special Charge Configurations

A thin spherical shell of radius 12 cm has a total charge of \( 9 \, \mu\text{C} \). What is the electric field at 15 cm

**Symmetric configurations** from Gauss's law produce characteristic fields. Uniformly charged infinite plane gives uniform field E = σ/(2ε₀) independent of distance due to planar symmetry, spherical shell acts as point charge outside E = kq/r² and zero inside, reflecting zero enclosed charge interior. Outside shell ( r > R ): E = (k q/r²) . k = 9 × 10⁹ N·m²/C² , q = 9 × 10⁻⁶ C , r = 0.15 m . E = 9 × 10⁹ × (9 × 10⁻⁶/(0.15)²) = 9 × 10⁹ × (9 × 10⁻⁶/0.0225) = 3.6 × 10⁶ N/C . Substituting values gives 3.6 × 10⁶ N/C, which

Ref: NCERT > Physics Book > Electric Charges and Fields > Field Due to Special Charge Configurations

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Field Due to Special Charge Configurations

A thin spherical shell of radius 8 cm has \( q = 4 \, \mu\text{C} \). What is the electric field at 6 cm from the center

**Field due to infinite plane and shells** illustrates symmetry power. Infinite plane's field remains constant because distant contributions balance, while spherical shell interior field cancels symmetrically, leading to E = 0 inside, E = kQ/r² outside. Inside shell ( r < R ): E = 0 (Gauss’s law). Substituting values gives 0 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, NEET and CUET.

Ref: NCERT > Physics Book > Electric Charges and Fields > Field Due to Special Charge Configurations

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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

A point charge \( 12 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 8 m along the x

**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 = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 12 × 10⁻⁶ C , r = 8 m . E = 9 × 10⁹ × (12 × 10⁻⁶/(8)²) = 9 × 10⁹ × (12 × 10⁻⁶/64) = 1.6875 × 10³ N/C . Substituting values gives 1.69 × 10³ 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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