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#charge separation

13 public questions tagged with this topic.

Conductors, Electrostatic Shielding and Dielectrics

Why does the potential energy of a system of two charges depend only on their separation and not on their orientation in

**Electrostatic shielding** inside hollow conducting shell field zero when no charges inside, regardless of external field, because free charges redistribute on outer surface to cancel external field inside conductor, E=0 inside material in equilibrium, consequence of Gauss's law and conductor property. The potential energy between two point charges is U = (1/4 π ε₀) (q₁ q₂/r) , where r is the distance between them. This expression depends only on the magnitude of the separation r , not on the direction or orientation of the line joining the charges in space, because the Coulomb force is isotr

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Conductors, Electrostatic Shielding and Dielectrics

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Conductors, Electrostatic Shielding and Dielectrics

Two charges \( 5 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are placed 10 cm apart. What is the potential energy of t

**Dielectric polarization** when slab inserted, bound charges appear reducing effective field, capacitance increases by factor K, potential difference for constant charge V = Q/C decreases, for constant voltage charge increases. Dielectric constant K = ε/ε₀ >1, e.g., K≈5 for glass. U = (1/4 π ε₀) (q₁ q₂/r) = 9 × 10⁹ × (5 × 10⁻⁶ × (-5 × 10⁻⁶)/0.1) = 9 × 10⁹ × (-25 × 10⁻¹²/0.1) = -2.25 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 -2.25 J follows, reflecting potential-capacitance relations.

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Conductors, Electrostatic Shielding and Dielectrics

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Potential Energy of System of Charges

Two charges \( 10 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are placed 20 cm apart. What is the potential energy of

**Potential energy of two charges** U = k q₁ q₂/r, k=9×10⁹ N·m²/C², q₁,q₂ in coulombs, r separation (m), positive for like charges (repulsive, work needed to bring together), negative for opposite (attractive, work released). For 20 μC and -8 μC, 0.2 m apart, U=9×10⁹×20×10⁻⁶×(-8×10⁻⁶)/0.2= -7.2 J. U = (1/4 π ε₀) (q₁ q₂/r) = 9 × 10⁹ × (10 × 10⁻⁶ × (-5 × 10⁻⁶)/0.2) = 9 × 10⁹ × (-50 × 10⁻¹²/0.2) = -2.25 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

Ref: NCERT > Physics Book > Electrostatic Potential and Capacitance > Potential Energy of System of Charges

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Superposition Principle and Equilibrium of Charges

Two charges \( +15 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are 75 cm apart. What is the distance from \( +15 \, \m

**Independent action of charges** allows total force or field as vector sum. Geometry dictates distances to evaluation point, and resultant follows Σ k q_i/r_i², explaining zero field at symmetric centres for equal charges. Let x be distance from +15 μC , then 0.75 - x from -5 μC . (15 × 10⁻⁶/x²) = (5 × 10⁻⁶/(0.75 - x)²) , 15 (0.75 - x)² = 5 x² . 3 (0.5625 - 1.5 x + x²) = x² , 1.6875 - 4.5 x + 3 x² = x² . 2 x² - 4.5 x + 1.6875 = 0 , x = (4.5 ± √(20.25 - 13.5)/4) =

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

Two charges \( +6 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) are 25 cm apart. What is the distance from \( +6 \, \mu\

**Coulomb's law** gives force between point charges as F = k·|q₁q₂|/r², k = 1/(4π ε₀) = 9×10⁹ N·m²/C², directed along line joining charges. Like charges repel, opposite attract, magnitude scales with product of charges and inverse square of separation r². Let distance from +6 μC be x , then from -4 μC is 0.25 - x . (k × 6 × 10⁻⁶/x²) = (k × 4 × 10⁻⁶/(0.25 - x)²) . (6/x²) = (4/(0.25 - x)²) , 6 (0.25 - x)² = 4 x² . 6 (0.0625 - 0.5 x + x²) = 4 x² , 0.375 - 3 x + 6 x² = 4

Ref: NCERT > Physics Book > Electric Charges and Fields > Coulomb's Law and Force Between Point Charges

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Coulomb's Law and Force Between Point Charges

In an experiment, a charged object is brought near a neutral conductor, causing charge separation. What phenomenon is re

**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. Electrostatic induction occurs when a charged object induces a separation of charges in a neutral conductor. The electric field of the charged object attracts opposite charges and repels like charges, redistributing them without direct contact. Substituting values gives Electrostatic induction, which matches expected magnitude for this electrostatic configuration, confirming C

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

A dipole has charges \( +q = 3 \, \mu\text{C} \) and \( -q = -3 \, \mu\text{C} \) separated by 2 mm. What is the dipole

**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°. Dipole moment: p = q × 2a , where 2a = 2 × 10⁻³ m , q = 3 × 10⁻⁶ C . p = 3 × 10⁻⁶ × 2 × 10⁻³ = 6 × 10⁻⁹ C m . Substituting values gives 6 × 10⁻⁹ 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 Dipole - Moment, Field and Torque

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Coulomb's Law and Force Between Point Charges

Two charges \( +5 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are 30 cm apart. What is the potential energy of the sys

**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. Potential energy: U = k (q₁ q₂/r) . U = 9 × 10⁹ × ((5 × 10⁻⁶) × (-5 × 10⁻⁶)/0.3) = 9 × 10⁹ × (-25 × 10⁻¹²/0.3) = -0.75 J . Substituting values gives -0.75 J, 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

A dipole with charges \( +4 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) separated by 2 mm is in a field \( 7 \times 10

**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. Dipole moment: p = q × 2a = 4 × 10⁻⁶ × 2 × 10⁻³ = 8 × 10⁻⁹ C m . Torque: tau = p E sin θ = 8 × 10⁻⁹ × 7 × 10⁴ × sin 30° = 5.6 × 10⁻⁴ × 0.5 = 2.8 × 10⁻⁴ N m . Substituting values gives 2.8 × 10⁻⁴ N 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 Dipole - Moment, Field and Torque

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Electrophoresis

What is the primary factor responsible for DNA separation in electrophoresis?

In electrophoresis, migration depends on charge to mass ratio and molecular sieving. DNA possesses a uniform negative charge due to phosphate backbone, one per nucleotide, resulting in nearly identical charge/mass ratio for all fragments. Consequently, in free solution, all DNA migrates equally. Separation in agarose or polyacrylamide occurs due to frictional resistance of the porous matrix, where longer molecules experience greater retardation. Thus, although labeled as size-based separation, the underlying principle involves differential mobility governed by charge/mass ratio interacting wit

Ref: NCERT Biology Class XII Principles on Klenow fill-in labeling, Lehninger Chapter 9 DNA cloning techniques, and Molecular Cloning by Sambrook Chapter 10 documenting end-labeling of cohesive termini.

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Electrophoresis

In isoelectric focusing, separation is based on:

Isoelectric focusing separates macromolecules based on differences in isoelectric point rather than solely molecular weight or total charge at fixed pH. A stable pH gradient is created using carrier ampholytes or immobilines immobilized in gel matrix. Proteins migrate under electric field until reaching zone where local pH equals pI, resulting in zero net charge and cessation of movement. This focusing concentrates proteins into extremely narrow bands at characteristic pH values. Distinction from SDS-PAGE which separates by size, or ion-exchange which separates by constant charge, underlies it

Ref: NCERT Biology Class XII Principles on Klenow fill-in labeling, Lehninger Chapter 9 DNA cloning techniques, and Molecular Cloning by Sambrook Chapter 10 documenting end-labeling of cohesive termini.

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