Electrostatics - Important Formulas Table

Electrostatics - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Coulomb’s Law	$𝐹=𝑘\frac{{𝑞}_1{𝑞}_2}{{𝑟}^2}$	$𝑘=\frac{1}{4𝜋{𝜖}_0}=9\times {10}^9$ Nm²/C²
2	Electric Field due to Point Charge	$𝐸=𝑘\frac{𝑞}{{𝑟}^2}$ (Magnitude)	Direction: away from +q, towards -q
3	Electric Field due to Dipole (Axial)	${𝐸}_{\text{axial}}=\frac{2𝑘𝑝}{{𝑟}^3}$	For r >> d
4	Electric Field due to Dipole (Equatorial)	${𝐸}_{\text{equatorial}}=\frac{𝑘𝑝}{{𝑟}^3}$	Direction opposite to dipole moment
5	Electric Flux	$𝜙=\overrightarrow{𝐸}\cdot \overrightarrow{𝐴}=𝐸𝐴\cos 𝜃$	SI unit: Nm²/C
6	Gauss’s Law	$𝜙=\frac{{𝑞}_{\text{enclosed}}}{{𝜖}_0}$	For closed surface
7	Electric Field due to Infinite Line Charge	$𝐸=\frac{𝜆}{2𝜋{𝜖}_0𝑟}$	λ = linear charge density
8	Electric Field due to Infinite Sheet	$𝐸=\frac{𝜎}{2{𝜖}_0}$	σ = surface charge density
9	Electric Potential (Point Charge)	$𝑉=𝑘\frac{𝑞}{𝑟}$	Scalar quantity
10	Potential due to Dipole	$𝑉=𝑘\frac{𝑝\cos 𝜃}{{𝑟}^2}$	-
11	Electric Potential Energy (Two Charges)	$𝑈=𝑘\frac{{𝑞}_1{𝑞}_2}{𝑟}$	-
12	Potential Energy of Dipole in E-field	$𝑈=-\overrightarrow{𝑝}\cdot \overrightarrow{𝐸}=-𝑝𝐸\cos 𝜃$	Minimum at θ = 0°
13	Torque on Dipole in E-field	$\overrightarrow{𝜏}=\overrightarrow{𝑝}\times \overrightarrow{𝐸}$	τ = pE sinθ
14	Capacitance of Parallel Plate Capacitor	$𝐶=\frac{{𝜖}_0𝐴}{𝑑}$	-
15	Capacitance with Dielectric	$𝐶=\frac{𝐾{𝜖}_0𝐴}{𝑑}$	K = dielectric constant
16	Equivalent Capacitance (Series)	$\frac{1}{{𝐶}_{𝑒𝑞}}=\frac{1}{{𝐶}_1}+\frac{1}{{𝐶}_2}+\dots$	-
17	Equivalent Capacitance (Parallel)	${𝐶}_{𝑒𝑞}={𝐶}_1+{𝐶}_2+\dots$	-
18	Energy Stored in Capacitor	$𝑈=\frac{1}{2}𝐶{𝑉}^2=\frac{1}{2}\frac{{𝑄}^2}{𝐶}=\frac{1}{2}𝑄𝑉$	Three equivalent forms
19	Electric Field between Plates	$𝐸=\frac{𝑉}{𝑑}=\frac{𝜎}{{𝜖}_0}$	For parallel plates
20	Force between Plates of Capacitor	$𝐹=\frac{{𝑄}^2}{2{𝜖}_0𝐴}$	Attractive force