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Kumar Rohan

Physics and Mathematics

Electrostatics — Complete Formula

⭐ – Most used in JEE
⚠️ – Common Mistake
💡 – Memory Hint

Coulomb’s Law

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Electrostatic Force	[F = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q_1 q_2}{r^2}]	[F] = force, [q_1, q_2] = charges, [r] = distance, [\varepsilon_0] = permittivity	N	Inverse square law ⭐
In Medium	[F = \dfrac{1}{4\pi\varepsilon} \dfrac{q_1 q_2}{r^2}]	[\varepsilon] = permittivity of medium	N	Force reduces in medium ⚠️

💡 Memory Hint:
Force ∝ charge product / distance²

Electric Field

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Electric Field	[E = \dfrac{F}{q}]	[E] = electric field, [q] = test charge	N/C	Force per unit charge ⭐
Field due to Point Charge	[E = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q}{r^2}]	—	N/C	Radial field ⭐
Superposition	[\vec{E} = \vec{E}_1 + \vec{E}_2 + \dots]	—	—	Vector addition ⭐

💡 Memory Hint:
Field lines show direction of force

Electric Potential

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Potential	[V = \dfrac{W}{q}]	[V] = potential, [W] = work	V	Work per unit charge ⭐
Point Charge	[V = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q}{r}]	—	V	Scalar quantity ⭐
Relation	[E = -\dfrac{dV}{dr}]	—	—	Field from potential ⭐

💡 Memory Hint:
Potential = energy per unit charge

Potential Energy

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Two Charges	[U = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q_1 q_2}{r}]	[U] = potential energy	J	Positive for like charges ⚠️
System of Charges	[U = \sum \dfrac{1}{4\pi\varepsilon_0} \dfrac{q_i q_j}{r_{ij}}]	—	J	Sum over pairs

💡 Memory Hint:
Like charges → repel → positive energy

Electric Dipole

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Dipole Moment	[p = q \cdot 2a]	[p] = dipole moment, [2a] = separation	C·m	Vector quantity ⭐
Torque	[\tau = pE\sin\theta]	[\theta] = angle	N·m	Aligns with field ⭐
Potential	[V = \dfrac{1}{4\pi\varepsilon_0} \dfrac{p\cos\theta}{r^2}]	—	V	Along axis/equator

💡 Memory Hint:
Dipole → two equal & opposite charges

Gauss’s Law

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Gauss Law	[\Phi = \dfrac{Q_{enc}}{\varepsilon_0}]	[\Phi] = electric flux, [Q_{enc}] = enclosed charge	N·m²/C	Very important ⭐
Flux	[\Phi = EA\cos\theta]	[A] = area	—	Through surface

💡 Memory Hint:
Flux depends only on enclosed charge

Electric Field (Gauss Law Results)

System	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Infinite Line Charge	[E = \dfrac{\lambda}{2\pi\varepsilon_0 r}]	[\lambda] = charge/length	N/C	Cylindrical symmetry ⭐
Infinite Plane Sheet	[E = \dfrac{\sigma}{2\varepsilon_0}]	[\sigma] = charge/area	N/C	Constant field ⭐
Solid Sphere (outside)	[E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^2}]	—	N/C	Like point charge
Solid Sphere (inside)	[E \propto r]	—	—	Linear variation ⚠️

💡 Memory Hint:
Use Gauss law only for high symmetry

Capacitance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Capacitance	[C = \dfrac{Q}{V}]	[C] = capacitance	F	Ability to store charge ⭐
Parallel Plate	[C = \dfrac{\varepsilon_0 A}{d}]	[A] = area, [d] = separation	F	Basic formula ⭐
With Dielectric	[C = K \dfrac{\varepsilon_0 A}{d}]	[K] = dielectric constant	F	Increases capacitance ⭐

💡 Memory Hint:
Capacitance ∝ area / separation

Combination of Capacitors

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Series	[\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}]	—	F	Like resistors in parallel ⭐
Parallel	[C_{eq} = C_1 + C_2]	—	F	Like resistors in series ⭐

💡 Memory Hint:
Series ↓ capacitance
Parallel ↑ capacitance

Energy Stored in Capacitor

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Energy	[U = \dfrac{1}{2}CV^2]	[U] = energy	J	Most used ⭐
Alternate	[U = \dfrac{1}{2}QV = \dfrac{Q^2}{2C}]	—	J	Use as needed

💡 Memory Hint:
Energy stored in electric field

Energy Density

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Energy Density	[u = \dfrac{1}{2}\varepsilon_0 E^2]	[u] = energy per volume	J/m³	Field energy ⭐

💡 Memory Hint:
Energy ∝ square of field

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