This chapter explains electrostatic potential and capacitance, providing essential concepts necessary for understanding electric fields and energy storage in capacitors.
ELECTROSTATIC POTENTIAL AND CAPACITANCE – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the ELECTROSTATIC POTENTIAL AND CAPACITANCE chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
V = k * Q / r
V is the electrostatic potential (V), k is Coulomb's constant (8.99 × 10⁹ Nm²/C²), Q is the point charge (C), and r is the distance from the charge to the point (m). This formula defines potential due to a point charge.
U = k * (q₁ * q₂) / r
U represents potential energy (J), q₁ and q₂ are point charges (C), and r is the distance between them (m). This shows how the potential energy between two point charges depends on their magnitudes and separation.
V = W / q
V is the electric potential (V), W is the work done (J), and q is the charge (C). This relates potential to work done in moving a charge in an electric field.
E = -dV/dx
E is the electric field (N/C), dV is the change in electric potential (V), and dx is the change in position (m). This indicates how the electric field relates to the gradient of the potential.
C = Q / V
C is the capacitance (F), Q is the charge (C), and V is the voltage (V). This defines capacitance as the ratio of charge stored to the potential difference.
C = ε₀(A/d)
C is the capacitance (F), ε₀ is the permittivity of free space (8.85 × 10⁻¹² F/m), A is the area of one plate (m²), and d is the distance between the plates (m). This shows the capacitance of a parallel plate capacitor.
U = 1/2 CV²
U is the energy stored (J), C is the capacitance (F), and V is the voltage (V). This equation calculates the energy stored in a capacitor.
U = qV
U represents the potential energy (J), q is the charge (C), and V is the potential (V). This relates the charge and potential to the energy stored.
V = k * (q / r) for multiple charges
This states that the total potential V at a point is the algebraic sum of the potentials due to individual charges q at distances r.
E = σ / ε₀
E is the electric field (N/C), σ is the surface charge density (C/m²), and ε₀ is the permittivity of free space. This defines the electric field generated by a charged surface.
Equations
V_{P-R} = V_P - V_R = -W_{RP} / q
This equation expresses the potential difference between points P and R in terms of work done against the electric field.
Φ = ∫ E · dA
Φ is the electric flux (N·m²/C), E is the electric field (N/C), and dA is the area element (m²). This calculates the total electric flux through a surface.
V = k * ∑ (q_i / r_i)
This is the potential at a point due to multiple charges, where q_i are individual charges and r_i are their distances from the point.
W = qEd
W is the work done (J), q is the charge (C), E is the electric field (N/C), and d is the displacement (m). This relates work done to charge moved in an electric field.
C_{eff} = C_1 + C_2 + ... (parallel)
This states that total capacitance for capacitors in parallel is the sum of individual capacitances.
1/C_{eff} = 1/C_1 + 1/C_2 + ... (series)
This states that total capacitance for capacitors in series is the reciprocal of the sum of the reciprocals of individual capacitances.
E = ΔV / d
E is the electric field (N/C), ΔV is the potential difference (V), and d is the separation between plates (m). This relates the electric field to the potential gradient.
p = q * 2a
p is the dipole moment (C·m), q is the charge (C), and 2a is the distance between the charges. This defines the dipole moment.
U_dipole = -p • E
This describes the potential energy of a dipole in an electric field, where p is the dipole moment and E is the electric field.
E_{surface} = σ/ε₀
E_{surface} is the electric field at the surface of a charged conductor, σ is surface charge density, and ε₀ is the permittivity of free space.
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