Electrostatics Formula

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
• ε: 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,
• ε 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 is the permittivity of free space
• R and R 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
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