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 – [ M0 L0 T1 A1 ]
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 × 109 N m2 C-2)
- q1, q2: 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 × 109 N m2 C-2)
- F: Force experienced by the charge
- qo: Test charge
Electric Field due to a Point Charge:
E = k{q\over r^2}
- E: Electric field strength
- k: Coulomb’s constant (9 × 109 N m2 C-2)
- q: Magnitude of the charge
- r: Distance from the charge
Electric Field due to a System of Charges:
E = Σ( Ei ) = kΣ {q_i\over {r_i}^2}
- E: Electric field strength at a point
- Σ: Summation of electric field strengths due to individual charges
- Ei: Electric field strength due to the i-th charge
- qi: Magnitude of the i-th charge
- ri: 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
- ε₀: Permittivity of free space (8.85 × 10-12 C2 N-1 m-2)
Electric Potential:
V = k{q \over r}
- V: Electric potential
- k: Coulomb’s constant (9 × 109 N m2 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
- Vb: Electric potential at point b
- Va: Electric potential at point a
Electric Potential due to a System of Charges:
V = Σ( Vi ) = k{q_i \over r_i}
- V: Electric potential at a point
- Σ: Summation of electric potentials due to individual charges
- Vi: Electric potential due to the i-th charge
- qi: Magnitude of the i-th charge
- ri: 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}- Ceq: Equivalent capacitance of capacitors in series
- C1, C2 and C3: Capacitances of individual capacitors
Capacitors in Parallel:
Ceq = C1 + C2 + C3
- Ceq: Equivalent capacitance of capacitors in parallel
- C1, C2, C3, : Capacitances of individual capacitors
Capacitance of a parallel plate capacitor:
C = ε_₀A\over d
- where C is the capacitance,
- ε₀ 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,
- ε₀ is the permittivity of free space
- R₁ and R₂ 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
