Electrostatics
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
CrackIt
Fundamental Laws & Fields
Coulomb's Law
F = k |q₁q₂| / r²
k = 1 / (4πε₀) ≈ 9×10⁹ Nm²/C²
k = 1 / (4πε₀) ≈ 9×10⁹ Nm²/C²
Force between two point charges. Vector form: F₁₂ = k(q₁q₂/r³) r₁₂
Electric Field (Point Charge)
E = F / q₀ = k|q| / r²
Force per unit test charge. Direction is radially outward for +q, inward for -q.
Superposition Principle
Fnet = Σ Fᵢ
Enet = Σ Eᵢ
Enet = Σ Eᵢ
Net force/field is the vector sum of individual forces/fields.
Electric Field (Continuous)
E = ∫ dE = ∫ (k dq / r²)
Integrate over the entire charge distribution.
Field of Infinite Line Charge
E = λ / (2πε₀r)
λ is linear charge density (C/m).
Field of Infinite Sheet
E = σ / (2ε₀)
σ is surface charge density (C/m²). Field is uniform.
Electric Potential & Energy
Electric Potential (Point Charge)
V = kq / r
Scalar quantity. Work done to bring a unit charge from ∞ to a point.
Potential Energy (2 Charges)
U = k q₁q₂ / r
Energy of the system. For multiple charges, sum U for all unique pairs.
Work-Energy Relation
Wext = ΔU = qΔV
Wfield = -ΔU = -qΔV
Wfield = -ΔU = -qΔV
ΔV = V_final - V_initial. Work done by external agent vs electric field.
Relation between E and V
E = -dV/dr
ΔV = -∫ E ⋅ dr
ΔV = -∫ E ⋅ dr
Electric field points in the direction of the steepest decrease in potential.
Gauss's Law & Dipoles
Electric Flux & Gauss's Law
Φ = ∫ E ⋅ dA = q_enclosed / ε₀
Net electric flux through a closed surface depends only on the enclosed charge.
E-Field of Spherical Shell
Ein = 0
Eout = kq / r²
Eout = kq / r²
For a uniformly charged thin spherical shell of radius R and charge q (for r > R).
Electric Dipole Moment
p = q × 2a
Vector from -q to +q. 2a is the separation distance.
Dipole Field & Torque
Eaxial = 2kp/r³
Eeq = kp/r³
τ = p × E = pE sinθ
Eeq = kp/r³
τ = p × E = pE sinθ
Torque τ tends to align the dipole with the external field E.
Capacitance & Dielectrics
Capacitance
C = Q / V
Unit: Farad (F)
Unit: Farad (F)
Ability to store charge. Depends on geometry, not Q or V.
Parallel Plate Capacitor
C = ε₀A / d
A is plate area, d is separation. For spherical C = 4πε₀R.
Energy Stored in Capacitor
U = ½CV² = Q²/2C = ½QV
Energy is stored in the electric field between the plates.
Effect of Dielectric (K)
C' = KC
E' = E/K
V' = V/K
E' = E/K
V' = V/K
Dielectric constant K > 1. Increases capacitance.
BITSAT Speed Hacks
For symmetrical charge distributions, E or V at the center is often zero. Always check symmetry first!
Use k = 9×10⁹ Nm²/C² and 1/4πε₀ interchangeably for rapid calculation.
Capacitor problems: If battery is disconnected, Q is constant. If connected, V is constant.
For dipoles, remember |E_axial| = 2|E_equatorial| for the same distance r.
Gauss's Law is your best friend for symmetric charge distributions (sphere, cylinder, sheet). Avoid integration if possible.
In capacitor combinations, look for Wheatstone bridge symmetry (C₁/C₂ = C₃/C₄) to simplify the circuit.
Capacitor Combinations
Series Combination
1/Ceq = 1/C₁ + 1/C₂ + ...
Charge (Q) is same on all capacitors. Voltage (V) divides.
Parallel Combination
Ceq = C₁ + C₂ + ...
Voltage (V) is same across all capacitors. Charge (Q) divides.
Key Comparisons: E vs. V
| Property | Electric Field (E) | Electric Potential (V) |
|---|---|---|
Nature | Vector | Scalar |
Formula (Point Charge) | k|q| / r² | kq / r |
SI Unit | N/C or V/m | V or J/C |
Inside Conductor (Static) | E = 0 | V = Constant |
Due to Dipole (r dependence) | ∝ 1/r³ | ∝ 1/r² |