Electrostatics

🟢 Lite — Quick Review

Rapid summary for last-minute revision before your exam.

Electrostatics — Key Facts for BUET Coulomb’s Law: F = kq₁q₂/r² where k = 1/(4πε₀) = 9×10⁹ Nm²/C² Electric field: E = F/q = kQ/r² (point charge); direction away from positive, toward negative Electric potential: V = kQ/r (point charge); 1V = 1J/C Capacitance: C = Q/V; energy stored: U = ½CV² = ½QV² = ½Q²/C ⚡ Exam tip: BUET electrostatics problems often combine Coulomb’s law with equilibrium — draw force diagrams carefully!

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🟡 Standard — Core Study

Standard content for students with a few days to months.

Electrostatics — BUET Study Guide

Coulomb’s Law: F = kq₁q₂/r² where k = 9×10⁹ Nm²/C² Vector form: F₁₂ = kq₁q₂(r₂−r₁)/|r₂−r₁|³ Inverse square law: force ∝ 1/r²

Electric field: E = F/q = kQ/r² (for point charge) Direction: radially outward from positive charge, inward toward negative charge Superposition: E_net = Σ E_i for multiple charges

Electric potential: V = W/q = kQ/r (for point charge) Potential difference: ΔV = V₂ − V₁ = −∫ E·dl Scalar quantity — superpose algebraically

Relationship between E and V: E = −dV/dr (in spherical symmetry) E = −∇V (general) For uniform field: E = V/d

Work done by electric field: W = q(V₁ − V₂) = qΔV For positive charge moving in direction of field: W is negative (potential energy increases)

Conductors in electrostatics:

• Electric field inside conductor = 0
• All charge resides on surface
• Surface charge density higher at sharp points
• E just outside surface = σ/ε₀ (perpendicular)

Capacitors:

• C = Q/V = ε₀A/d (parallel plate)
• Series: 1/C_eq = Σ 1/C_i
• Parallel: C_eq = Σ C_i

Energy stored in capacitor: U = ½QV = ½CV² = ½Q²/C Energy density in electric field: u = ½ε₀E²

Electric dipole: Moment: p = qd (vector from − to +) Torque in uniform field: τ = pE sin θ Potential at point on axial line: V = kp/r² Field at axial point: E = 2kp/r³

• Key formula: F = kq₁q₂/r²; E = kQ/r²; V = kQ/r; C = Q/V; U = ½CV²
• Common trap: E is a vector, V is a scalar — for superposition, add vectors for E, add scalars for V
• Exam weight: 2–3 questions per exam (8–12 marks); very high weight in BUET

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🔴 Extended — Deep Dive

Comprehensive coverage for students on a longer study timeline.

Electrostatics — Comprehensive BUET Notes

Continuous charge distributions:

• Linear charge density: λ = Q/L (C/m)
• Surface charge density: σ = Q/A (C/m²)
• Volume charge density: ρ = Q/V (C/m³)

Field from continuous distribution: dE = k dq r̂/r²; integrate over distribution For ring on axis: E = kQx/(x²+R²)^{3/2} along axis For disc on axis: E = (σ/2ε₀)[1 − x/√(x²+R²)] along axis

Potential from continuous distribution: V = ∫ k dq/r

Gauss’s Law: ∮ E·dA = Q_enclosed/ε₀ Useful for symmetric charge distributions

Applications of Gauss’s Law:

• Point charge: E = kQ/r²
• Infinite plane: E = σ/(2ε₀)
• Infinite cylinder: E = λ/(2πε₀r)
• Solid sphere (uniform charge): for r > R: E = kQ/r²; for r < R: E = kQr/R³

Electric dipole in uniform field: Torque: τ = pE sin θ (vector τ = p × E) Equilibrium: θ = 0 or π (aligned with field) PE in field: U = −pE cos θ = −p·E

Dipole in non-uniform field: Experiences force in direction of increasing field strength Also experiences torque

Method of images: For point charge near grounded conducting plane: Image charge = −q at mirror position Field above plane same as two charges

Capacitor combinations: Series: Q same on all capacitors; V divides Parallel: V same on all capacitors; Q divides

Dielectrics:

• Dielectric constant κ = ε/ε₀
• For dielectric-filled capacitor: C = κC₀
• Energy stored: U = ½κε₀E² × volume

Force between capacitor plates: F = ½QE = ½ε₀E²A (attractive) Derived from energy: F = dU/dd = ½QV²/d²

Equilibrium of charges: For three charges in equilibrium: use Coulomb’s law to set forces = 0 Usually one charge at midpoint or on line between other two

Spark discharge: Electric breakdown of air: E_max ≈ 3×10⁶ V/m When E exceeds this, air conducts

Capacitor with dielectric:

• Stored charge: Q = CV
• Induced charge on dielectric: Q_ind = Q(1 − 1/κ)
• Effective capacitance: C_eff = κC₀

Energy in dielectric: When inserting dielectric at constant V: work done by battery = (κ − 1)½CV² When inserting at constant Q: work done = ½CV²(1/κ − 1)

Van de Graaff generator: Charge delivered to sphere: Q_max = R×E_max Maximum potential: V_max = R×E_max

Electric pressure on surface: P = ½σE (on charged conductor surface) E just outside = σ/ε₀, so P = σ²/(2ε₀)

• Remember: F = kq₁q₂/r²; E = F/q = kQ/r²; V = kQ/r; for series capacitors: Q same, V divides; for parallel: V same, Q divides
• Previous years: “Two charges +q and +4q at distance d. Find point where net field is zero” [2023 BUET]; “Find capacitance of parallel plate with d=1mm, area=100cm²” [2024 BUET]; “Energy stored in 10μF capacitor at 100V” [2024 BUET]

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📊 BUET Admission Exam Essentials

Detail	Value
Questions	Varies by year (~40-50 MCQ)
Time	Usually 2–3 hours
Marks	Varies by section
Subjects	Mathematics (highest weight), Physics, Chemistry
Negative	Usually no negative marking in BUET
Mode	Written + MCQ depending on year

🎯 High-Yield Topics for BUET Physics

• Mechanics (Laws of Motion, Work-Energy, Rotational) — very high weight
• Electrostatics and Current Electricity — very high weight
• Modern Physics (Photoelectric effect, Atoms) — high weight
• Heat and Thermodynamics — medium-high weight
• Optics (Reflection, Refraction) — medium weight

📝 Previous Year Question Patterns

• Electrostatics: 2–3 questions per exam, 8–12 marks
• Common patterns: Coulomb’s law, electric field and potential, capacitors, energy storage
• Weight: very high — one of the most important BUET physics topics

💡 Pro Tips

• Electric field is vector, potential is scalar — superposition differs
• For equilibrium problems, set net force on each charge = 0
• Capacitors in series: all have same charge; in parallel: all have same voltage
• Energy stored in capacitor: U = Q²/(2C) = ½CV² = ½QV
• For continuous charge distributions, use integration; for symmetric ones, try Gauss’s law first

🔗 Official Resources

• BUET Official
• BUET Admission Portal

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