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Cheat sheet · Class 12 · CBSE · Science Physics

ELECTRIC CHARGES AND FIELDS cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 12 · Physics

Cheat sheet

Chapter 1Electric Charges and Fields

Gauss: flux through a closed surface = enclosed charge / ε₀.

1. Charge

  • Quantised: q=neq = ne, e=1.6×10−19e = 1.6\times10^{-19} C.
  • Conserved and additive.
  • Like charges repel; unlike attract.

2. Coulomb's Law

F=14πε0q1q2r2F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}
14πε0=9×109 N m2C−2\dfrac{1}{4\pi\varepsilon_0} = 9\times10^9\ \text{N m}^2\text{C}^{-2}

In a medium, force is reduced by the dielectric constant K.

3. Electric Field

SourceField E
Point chargekqr2\dfrac{kq}{r^2}
Dipole, axial2kpr3\dfrac{2kp}{r^3}
Dipole, equatorialkpr3\dfrac{kp}{r^3} (opposite to p)
Infinite line chargeλ2πε0r\dfrac{\lambda}{2\pi\varepsilon_0 r}
Infinite plane sheetσ2ε0\dfrac{\sigma}{2\varepsilon_0}
Spherical shell (outside / inside)kqr2\dfrac{kq}{r^2} / 0

Dipole moment p=q×2ap = q\times2a; torque in field τ=pEsin⁡θ\tau = pE\sin\theta.

4. Gauss's Law

ϕ=∮E⃗⋅dA⃗=qencε0\phi = \oint\vec E\cdot d\vec A = \dfrac{q_{enc}}{\varepsilon_0}

5. Key Points

  • Field lines never cross.
  • Lines start on + and end on − charges.
  • Net force on a dipole in uniform field = 0.
  • Charging by induction needs no contact.

Remember: Coulomb | E of dipole, line, sheet | Gauss

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