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CLASS 12 • PHYSICS
Electric Charges & Fields
1. Basic Properties
Quantization
$Q = \pm ne$
Conservation
$\sum Q_{in} = \sum Q_{fin}$
2. Coulomb's Law
Force in Vacuum
$F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$
Vector Form
$\vec{F}_{12} = \frac{k q_1 q_2}{r^3} \vec{r}_{21}$
Dielectric Constant
$K = F_{air}/F_{med}$
3. Electric Field
Point Charge
$E = \frac{kQ}{r^2}$
Force on Charge (Important)
$\vec{F} = q\vec{E}$
Acceleration $a = \frac{qE}{m}$
Charge Densities
$\lambda = Q/L$ (Line)
$\sigma = Q/A$ (Surface)
$\rho = Q/V$ (Volume)
$\sigma = Q/A$ (Surface)
$\rho = Q/V$ (Volume)
4. Electric Dipole
Dipole Moment ($\vec{p}$)
$\vec{p} = q(2\vec{a})$
Dir: -ve to +ve
Axial Field
$E_{ax} = \frac{2kp}{r^3}$
Equatorial Field
$E_{eq} = \frac{kp}{r^3}$
5. Torque & Energy
Torque
$\vec{\tau} = \vec{p} \times \vec{E} = pE\sin\theta$
Potential Energy
$U = -pE \cos\theta$
Equilibrium Conditions
Stable: $\theta = 0^\circ$ ($U = -pE$)
Unstable: $\theta = 180^\circ$ ($U = +pE$)
Work Done
$W = pE(\cos\theta_1 - \cos\theta_2)$
6. Gauss's Law
Electric Flux ($\phi$)
$\phi_E = \oint \vec{E} \cdot d\vec{s} = EA \cos\theta$
Gauss's Theorem
$\oint \vec{E} \cdot d\vec{s} = \frac{q_{in}}{\epsilon_0}$
7. Applications
Infinite Wire
$E = \frac{\lambda}{2\pi\epsilon_0 r}$
Infinite Sheet
$E = \frac{\sigma}{2\epsilon_0}$
Spherical Shell
Inside ($r < R$): $E=0$
Surface ($r = R$): $E = \sigma/\epsilon_0$
Outside ($r > R$): $E = kQ/r^2$
8. Common Exam Traps
- ⚠️ The Angle Trap: In Torque ($\tau = pE \sin\theta$), $\theta$ is angle between Dipole ($\vec{p}$) and Field ($\vec{E}$), NOT with the surface.
- ⚠️ Distance Trap: For Dipoles, distance is $2a$. If total length is given as 10cm, then $2a = 10cm$ (Don't double it!).
- ⚠️ Unit Trap: Charge is often in $\mu C$. Always multiply by $10^{-6}$ before calculating Force.
9. Golden Theory Rules
- No Intersection: Two field lines NEVER intersect.
- Conductors: Electric Field inside a conductor is ALWAYS zero.
- Perpendicular: Field lines are always perpendicular to the surface.
- Loops: Electrostatic field lines do NOT form closed loops.
