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#electric charge

9 public questions tagged with this topic.

Energy Stored in Capacitor and Energy Density

A \( 8 \, \mu\text{F} \) capacitor is charged to \( 500 \, \text{V} \). What is the energy stored in it?

**Work done charging capacitor** is integral ∫ V dQ = ∫ Q/C dQ = Q²/2C, stored as electrostatic energy. When capacitor discharges, energy released as heat or work, explaining spark when shorted, energy proportional to V². U = (1/2) C V² = (1/2) × 8 × 10⁻⁶ × (500)² . U = (1/2) × 8 × 10⁻⁶ × 250000 = 1 J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V = Q_total/C_total, result 1 J follows, reflecting potential-capacitance relations.

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Energy Stored in Capacitor and Energy Density

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Energy Stored in Capacitor and Energy Density

In a system of two capacitors connected in series across a battery, why does the capacitor with smaller capacitance stor

**Energy density** in electric field u = ½ ε E², ε = K ε₀, E = V/d, total energy U = u·volume = ½ ε E²·A d =½ ε A d·(V/d)²=½ ε A V²/d=½ C V², consistent. For parallel plate, E = V/d ≈10⁶ V/m for 400 V across 0.4 mm, u≈½×8.85×10⁻¹²×10¹²≈4.4 J/m³. In series, the charge Q on each capacitor is the same. Energy stored in a capacitor is U = (Q²/2C) . For a smaller capacitance C , the denominator 2C is smaller, so U is larger compared to a capacitor with larger C . Alternatively, since V = (Q/C) , the smaller

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Energy Stored in Capacitor and Energy Density

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Energy Stored in Capacitor and Energy Density

A \( 6 \, \mu\text{F} \) capacitor is charged to \( 300 \, \text{V} \). What is the energy stored in it?

**Energy density** in electric field u = ½ ε E², ε = K ε₀, E = V/d, total energy U = u·volume = ½ ε E²·A d =½ ε A d·(V/d)²=½ ε A V²/d=½ C V², consistent. For parallel plate, E = V/d ≈10⁶ V/m for 400 V across 0.4 mm, u≈½×8.85×10⁻¹²×10¹²≈4.4 J/m³. U = (1/2) C V² = (1/2) × 6 × 10⁻⁶ × (300)² . U = (1/2) × 6 × 10⁻⁶ × 90000 = 0.27 J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V²

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Energy Stored in Capacitor and Energy Density

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Electric Dipole - Moment, Field and Torque

Which property of electric charge explains why the total charge of an isolated system remains constant even when objects

**Electric dipole** consists of charges +q and -q separated by 2a, dipole moment p = q·2a, vector from negative to positive, unit C·m. In uniform field E, torque τ = p × E, magnitude τ = p E sinθ, tending to align p with E, potential energy U = -p·E = -p E cosθ. The conservation of electric charge states that the total charge in an isolated system remains constant over time. When objects are rubbed together, charge is transferred from one to another (e.g., electrons move), but no new charge is created or destroyed. This ensures the net charge of the system stays the

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Dipole - Moment, Field and Torque

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Electric Dipole - Moment, Field and Torque

What property of electric charges explains why the smallest observable charge is that of an electron or proton?

**Interaction of dipole with uniform field** produces pure couple without net force, equal opposite forces forming torque. Potential energy minimum -pE at alignment, maximum +pE at anti-alignment, governing orientation dynamics. Quantization of charge means that charge exists in discrete units, with the smallest unit being the charge of an electron or proton ( e ). All observable charges are integer multiples of this fundamental unit, reflecting this property. Substituting values gives Quantization, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Dipole - Moment, Field and Torque

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Superposition Principle and Equilibrium of Charges

What property of electric charges explains why two objects with identical charges repel each other?

**Vector addition of forces** underlies multi-charge analysis. Each pair contributes independent Coulomb force, resultant obtained by resolving components along axes. Equilibrium occurs when vector sum vanishes, often at symmetric points where contributions balance. The polarity of charge (positive or negative) determines interaction: like charges repel due to the repulsive force described by Coulomb’s law, where the force direction depends on the sign of the charges, causing repulsion for identical signs. Substituting values gives Polarity, which matches expected magnitude for this electrosta

Ref: NCERT > Physics Book > Electric Charges and Fields > Superposition Principle and Equilibrium of Charges

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Coulomb's Law and Force Between Point Charges

A glass rod is rubbed with silk and acquires a charge of \( +2.5 \times 10^{-7} \, \text{C} \). How many electrons were

**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. Charge on glass rod is positive, so electrons are transferred from glass to silk. Charge of one electron e = -1.6 × 10⁻¹⁹ C . Number of electrons: n = (q/|e|) = (2.5 × 10⁻⁷/1.6 × 10⁻¹⁹) = 1.5625 × 10¹² . Substituting values gives 1.56 × 10¹², 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

What property of electric charges allows them to be treated as scalars despite their ability to attract or repel?

**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. The additivity of charges means their total value is the algebraic sum of individual charges, treating them as scalars with magnitude and sign (positive or negative). The directional forces (attraction/repulsion) arise from field interactions, not the charge itself. Substituting values gives Additivity, which matches expected magnitude

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

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Electric Charge, Quantization and Conservation

How many electrons must be added to a neutral body to give it a charge of \( -8 \times 10^{-8} \, \text{C} \)?

**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. q = n e , e = -1.6 × 10⁻¹⁹ C . n = (q/e) = (-8 × 10⁻⁸/-1.6 × 10⁻¹⁹) = 5 × 10¹¹ . Substituting values gives 5 × 10¹¹, 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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