## Electric Charges

Particles |
Charge |
Mass |

Electron |
-1.6 × 10^{-19 }C |
9.1 × 10^{-31 }kg |

Proton |
1.6 × 10^{-19 }C |
1.67×10^{−27} kg |

Neutron |
0 C | 1.67×10^{−27} kg |

**Formula:** Charge (Q) = n × e

- n = No of electron
- e = Charge of an electron

Unit of charge – Coulomb (C)

Dimension – [ M^{0} L^{0} T^{1} A^{1} ]

## Electric Current:

**Definition:** Electric current is the rate of flow of charge.

**Formula:** Current (I) = Charge\ (Q) \over time (t)

Unit – Ampere (A) or Coulomb / second

## Coulomb’s Law:

F = k{q_1q_2\over r^2}

- F: Force between two point charges
- k: Coulomb’s constant (9 × 10
^{9}N m^{2}C^{-2}) - q
_{1}, q_{2}: Magnitude of the charges - r: Distance between the charges

## Electric Field:

E = F\over q_o

- E: Electric field strength
- k: Coulomb’s constant (9 × 10
^{9}N m^{2}C^{-2}) - F: Force experienced by the charge
- q
_{o}: Test charge

## Electric Field due to a Point Charge:

E = k{q\over r^2}

- E: Electric field strength
- k: Coulomb’s constant (9 × 10
^{9}N m^{2}C^{-2}) - q: Magnitude of the charge
- r: Distance from the charge

## Electric Field due to a System of Charges:

E = Σ( E_{i }) = kΣ {q_i\over {r_i}^2}

- E: Electric field strength at a point
- Σ: Summation of electric field strengths due to individual charges
- E
_{i}: Electric field strength due to the i-th charge - q
_{i}: Magnitude of the i-th charge - r
_{i}: Distance from the i-th charge

## Electric Flux:

Φ = E × A × cos(θ)

- Φ: Electric flux
- E: Electric field strength
- A: Area vector, perpendicular to the surface
- θ: Angle between the electric field and the area vector

## Gauss’s Law:

Φ = q \over ε₀

- Φ: Electric flux through a closed surface
- q: Net charge enclosed by the surface
- ε
_{₀}: Permittivity of free space (8.85 × 10^{-12}C^{2}N^{-1}m^{-2})

## Electric Potential:

V = k{q \over r}

- V: Electric potential
- k: Coulomb’s constant (9 × 10
^{9}N m^{2}C^{-2}) - q: Magnitude of the charge
- r: Distance from the charge

## Potential Difference:

ΔV = Vb – Va

- ΔV: Potential difference between points b and a
- V
_{b}: Electric potential at point b - V
_{a}: Electric potential at point a

## Electric Potential due to a System of Charges:

V = Σ( V_{i} ) = k{q_i \over r_i}

- V: Electric potential at a point
- Σ: Summation of electric potentials due to individual charges
- V
_{i}: Electric potential due to the i-th charge - q
_{i}: Magnitude of the i-th charge - r
_{i}: Distance from the i-th charge

## Equipotential Surfaces:

- Equipotential surfaces are surfaces in an electric field where the electric potential is constant.
- Electric field lines are always perpendicular to equipotential surfaces.

## Capacitance:

C = Q \over V

- C: Capacitance
- Q: Charge stored in the capacitor
- V: Potential difference across the capacitor

## Capacitors in Series:

{1 \over C_{eq}} = {1 \over C_1} + {1 \over C_2} + {1 \over C_3}- C
_{eq}: Equivalent capacitance of capacitors in series - C
_{1}, C_{2}and C_{3}: Capacitances of individual capacitors

## Capacitors in Parallel:

C_{eq} = C_{1} + C_{2} + C_{3}

- C
_{eq}: Equivalent capacitance of capacitors in parallel - C
_{1}, C_{2}, C_{3}, : Capacitances of individual capacitors

## Capacitance of a parallel plate capacitor:

C = ε_₀A\over d

- where C is the capacitance,
- ε
_{₀}is the permittivity of free space, - A is the area of the plates,
- d is the separation between the plates.

## Capacitance of a spherical capacitor:

C = 4πε₀R_₁R_₂ \over (R_₂ - R_₁)

- C is the capacitance,
- ε
_{₀}is the permittivity of free space - R
_{₁}and R_{₂}are the radii of the inner and outer spheres.

## Electric field between the plates of a parallel plate capacitor:

E = V\over d

- E is the electric field,
- V is the potential difference,
- d is the separation between the plates.

## Potential difference across a parallel plate capacitor:

V = {Q\over C}- V is the potential difference
- Q is the charge stored on the capacitor,
- C is the capacitance.

## Energy Stored in a Capacitor:

U = {1\over 2}×C×V^2

- U: Energy stored in the capacitor
- C: Capacitance
- V: Potential difference across the capacitor