Electrostatics and Current Electricity — NEET Physics

Electrodynamics is, with mechanics, one of the two largest blocks in NEET Physics — together electrostatics and current electricity contribute 4–5 questions almost every year. Electrostatics studies charges at rest (force, field, potential, capacitance); current electricity studies charges in motion (current, resistance, circuits, power). The two share one backbone: the inverse-square Coulomb force and the field-and-potential language built on it. This chapter derives each result and works it through, so circuit and field problems become routine.

Part A — Electrostatics

1. Charge and Coulomb's law

Charge is quantised ($q=ne$, $e=1.6\times 10^{-19}$ C) and conserved. Two point charges attract or repel with a force:

$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}=k\frac{q_1{q}_2}{r^2},k=9\times 10^9{\text{N⋅m}}^2/{\text{C}}^2$

• Inverse-square, like Newton's gravity — but far stronger, and both attractive and repulsive.
• Two 1 μC charges 1 m apart: $F=9\times 10^9\times \frac{(10^{-6}{)}^2}{1^2}=9\times 10^{-3}$ N. Double the separation → force to a quarter.

2. Electric field

The field is the force per unit positive charge — a vector that exists in space around a charge:

$\vec{E}=\frac{\vec{F}}{q},E=\frac{kQ}{r^2}$

• A 1 μC charge produces $E=9\times 10^9\times \frac{10^{-6}}{1^2}=9000$ N/C at 1 m.
• Field lines start on positive, end on negative charge; their density shows field strength; they never cross.
• Fields superpose as vectors from multiple charges.

3. Electric potential and potential energy

Potential is the potential energy per unit charge — a scalar (easier to add than field vectors):

$V=\frac{kQ}{r},U=qV,E=-\frac{dV}{dr}$

• Potential difference drives charge; work to move $q$ through $\Delta V$ is $W=q\Delta V$.
• Equipotential surfaces are everywhere perpendicular to field lines; no work is done moving along one.

4. Capacitance

A capacitor stores charge and energy. Capacitance relates charge to voltage:

$C=\frac{Q}{V},C_{\text{parallel-plate}}=\frac{{\epsilon }_{0}A}{d},E_{\text{stored}}=\frac{1}{2}C{V}^2$

Combinations:

• Parallel: $C=C_1+C_2$ (add directly). Two 2 μF → 4 μF.
• Series: $\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}$. Two 2 μF → 1 μF.
• A dielectric of constant $\kappa$ inserted between the plates multiplies $C$ by $\kappa$.

Note capacitors combine oppositely to resistors: capacitors add in parallel, resistors add in series.

Part B — Current Electricity

5. Current, Ohm's law and resistivity

Current is the rate of charge flow, carried by drifting electrons:

$I=\frac{q}{t},V=IR,R=\rho \frac{L}{A}$

• Ohm's law $V=IR$ holds for ohmic conductors at constant temperature.
• Resistance grows with length and falls with cross-section: doubling the length doubles $R$; doubling the area halves it. $\rho$ (resistivity) is the material property.
• Electrons drift slowly (mm/s) but the signal (field) propagates near light speed.

6. Resistors in series and parallel

$R_{\text{series}}=R_1+R_2+\cdots ,\frac{1}{R_{\text{parallel}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$

• Series current is the same through each; voltages add.
• Parallel voltage is the same across each; currents add. Two 6 Ω in parallel → 3 Ω; two equal $R$ in parallel → $R/2$.

7. Kirchhoff's laws

For any circuit:

1. Junction rule (KCL): charge is conserved, so total current in = total current out.
2. Loop rule (KVL): energy is conserved, so the sum of potential changes around any loop is zero.

Worked example 7.1. If 3 A and 2 A flow into a junction and one wire leaves it, the outgoing current is $3+2=5$ A (junction rule).

8. Electrical power and heating

$P=VI=I^{2}R=\frac{V^2}{R}$

• Choose the form matching what you know. A 100 W bulb rated at 200 V has $R=\frac{V^2}{P}=\frac{200^2}{100}=400$ Ω and draws $I=P/V=0.5$ A.
• Energy dissipated as heat is $I^{2}Rt$ (Joule heating) — the basis of heaters and fuses.

9. Cells, EMF and internal resistance

A real cell has internal resistance $r$, so its terminal voltage falls when it delivers current:

$V=\text{EMF}-Ir$

• A 6 V cell with $r=1$ Ω delivering 2 A has terminal voltage $V=6-2\times 1=4$ V.
• On open circuit ($I=0$) the terminal voltage equals the EMF.

10. The Wheatstone bridge

Four resistors in a bridge are balanced (no current through the galvanometer) when:

$\frac{P}{Q}=\frac{R}{S}$

• With $P=10$, $Q=20$, $S=40$: balance gives $R=\frac{P\cdot S}{Q}=\frac{10\times 40}{20}=20$ Ω.
• The meter bridge and potentiometer are practical forms — the potentiometer measures EMF without drawing current, so it beats a voltmeter for accuracy.

11. Common traps NEET sets here

• Capacitor vs resistor combination rules — capacitors add in parallel, resistors in series.
• Field (vector) vs potential (scalar) — add fields as vectors, potentials as scalars.
• Forgetting internal resistance — terminal voltage $<$ EMF whenever current flows.
• Using the wrong power form — pick $I^{2}R$, $V^2/R$ or $VI$ by what's given.
• Resistance scaling — $R=\rho L/A$: stretching a wire raises $R$; thickening lowers it.
• Field inside a conductor — it is zero in electrostatic equilibrium; charge resides on the surface.

12. Memory aids

• "Caps in parallel add, resistors in series add" — the mirror-image rule.
• "kQ over r² field, kQ over r potential" — one power of r apart.
• "EMF minus Ir" — terminal voltage droops under load.
• "P has three faces: VI, I²R, V²/R" — use whichever fits.
• "P/Q = R/S" — Wheatstone balance.

13. Exam protocol

1. Coulomb's law and field are inverse-square ($k{q}_1{q}_2/r^2$, $kQ/r^2$); potential is $kQ/r$.
2. Add fields as vectors, potentials as scalars.
3. Capacitors: parallel add, series reciprocal; energy $\frac{1}{2}C{V}^2$; dielectric ×$\kappa$.
4. Ohm's law $V=IR$; $R=\rho L/A$ scales with length/area.
5. Resistors: series add, parallel reciprocal.
6. Apply Kirchhoff's junction and loop rules for networks.
7. Power: pick $VI$, $I^{2}R$ or $V^2/R$; heat $=I^{2}Rt$.
8. Terminal voltage $V=\text{EMF}-Ir$; Wheatstone balance $P/Q=R/S$.