#point charge

Coulomb's Law and Force Between Point Charges

A point charge \( q = 5 \, \mu\text{C} \) is placed at the origin. What is the electric field magnitude at a point 2 m a

**Inverse-square law** for charges states F ∝ 1/r² while increasing with charge product. Using k = 9×10⁹ N·m²/C², force at distance r follows F = k q₁q₂/r², forming basis for pairwise force calculation. Electric field: E = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 5 × 10⁻⁶ C , r = 2 m . E = 9 × 10⁹ × (5 × 10⁻⁶/(2)²) = 9 × 10⁹ × (5 × 10⁻⁶/4) = 1.125 × 10⁴ N/C . Substituting values gives 1.125 × 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 > Coulomb's Law and Force Between Point Charges

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Electric Dipole - Moment, Field and Torque

Why does the electric field due to a dipole exhibit a stronger angular dependence compared to a single point charge?

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. The dipole’s field arises from two opposite charges, creating a directional dependence. The angle between the dipole axis and the point affects the field’s magnitude and direction more significantly than a point charge’s isotropic 1/r² field. Substituting values gives Directional dependence, 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 Dipole - Moment, Field and Torque

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Continuous Charge Distribution

Why does the electric field outside a charged conducting sphere resemble that of a point charge located at its center?

**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. The spherical symmetry of the charge distribution on the conductor’s surface ensures that the field outside behaves as if all charge were at the center, as per Gauss’s law. This symmetry simplifies the field to a radial, point-charge-like pattern. Substituting values gives Spherical symmetry, 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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Coulomb's Law and Force Between Point Charges

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

**Electrostatic force** described by F = (1/4π ε₀)·q₁q₂/r² obeys Newton's third law. Magnitude depends on q₁q₂ and 1/r², enabling quantitative estimation at given separation, with sign indicating attraction or repulsion. E = (k |q|/r²) . k = 9 × 10⁹ N·m²/C² , q = 10 × 10⁻⁶ C , r = 10 m . E = 9 × 10⁹ × (10 × 10⁻⁶/(10)²) = 9 × 10⁹ × (10 × 10⁻⁶/100) = 9 × 10² N/C . Substituting values gives 900 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 > Coulomb's Law and Force Between Point Charges

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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.