Summary

This sub-topic built up the WBCHSE Unit 1 account of electric charges and fields in the order the syllabus lists it. Electric charge (Section 1.2) obeys three defining properties: it is additive (net charge is a simple algebraic sum), conserved (never created or destroyed, only transferred), and quantised (always an integral multiple $ne$ of the elementary charge $e=1.6\times10^{-19}\ \text{C}$). Coulomb's law (Section 1.3), $F=kq_1q_2/r^2$ with $k=1/4\pi\epsilon_0\approx9\times10^9\ \text{N}\,\text{m}^2/\text{C}^2$, gives the force between two point charges, extended to many charges by the superposition principle (Section 1.4, vector addition of individual forces) and to smeared-out charge by the charge densities $\lambda$, $\sigma$, $\rho$ (Section 1.5).

The electric field $\vec{E}=\vec{F}/q_0$ (Section 1.6) reduces, for a point charge, to $E=kq/r^2$, and is pictured using electric field lines (Section 1.7): starting on positive charge, ending on negative charge, never crossing, and denser where the field is stronger.

The electric dipole, of moment $p=q(2a)$ directed from $-q$ to $+q$ (Section 1.8), produces a field that falls off as $1/r^3$: $E_{\text{axial}}=2kp/r^3$ along $\vec{p}$ on the axis (Section 1.9), $E_{\text{eq}}=kp/r^3$ opposite to $\vec{p}$ on the equatorial line -- exactly half the axial value (Section 1.10) -- and, at a general point making angle $\theta$ with the axis, $E=(kp/r^3)\sqrt{1+3\cos^2\theta}$, which correctly reduces to both special cases (Section 1.11). Placed in a UNIFORM external field $\vec{E}$, a dipole feels zero net force but a net torque $\tau=pE\sin\theta$, $\vec{\tau}=\vec{p}\times\vec{E}$, that tends to align $\vec{p}$ with $\vec{E}$ (Section 1.12). …