Electrostatics

Electric charge is a fundamental property of matter that comes in two kinds, positive and negative, with like charges repelling and unlike charges attracting. Charge is quantised ($q = ne$, where $e = 1.6\times10^{-19}\ \text{C}$) and conserved — it can be transferred but never created or destroyed. These two principles, along with the additive nature of charge, underlie almost every NEET conceptual question in this chapter.

Coulomb's law gives the force between two point charges: $F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^{2}}$, an inverse-square law much like gravitation but vastly stronger and capable of being attractive or repulsive. The constant $\dfrac{1}{4\pi\varepsilon_0} \approx 9\times10^{9}\ \text{N m}^{2}\text{C}^{-2}$. In a medium of dielectric constant $K$, the force is reduced by a factor $K$, since $\varepsilon = K\varepsilon_0$ — a frequently tested modification.

To describe the influence of a charge on its surroundings we use the electric field $\vec{E}$, the force per unit positive test charge: $\vec{E} = \dfrac{\vec{F}}{q_0}$. For a point charge, $E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^{2}}$, pointing away from a positive charge and towards a negative one. Fields from several charges add as vectors (the superposition principle), so the net field is found by adding contributions head-to-tail.

Field lines give a visual picture: they start on positive charges and end on negative ones, never cross, and crowd together where the field is strong. A useful NEET fact is that the field inside a charged conductor is zero in electrostatic equilibrium, and any excess charge resides entirely on its outer surface — the basis of electrostatic shielding.

An electric dipole is a pair of equal and opposite charges $\pm q$ separated by a small distance $2a$. Its strength and direction are captured by the dipole moment $\vec{p} = q(2a)$, pointing from the negative to the positive charge. The dipole is a key NEET model because polar molecules like water behave as dipoles.

The field of a dipole falls off faster than that of a point charge — as $1/r^{3}$. Along the axis the field is $E_{axial} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^{3}}$, while along the perpendicular bisector it is half this and oppositely directed, $E_{equatorial} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^{3}}$. In a uniform field a dipole feels no net force but a torque $\tau = pE\sin\theta$ that tries to align it with the field, with potential energy $U = -pE\cos\theta$.

Gauss's law is the most powerful tool in electrostatics. It states that the total electric flux through any closed surface equals the enclosed charge divided by $\varepsilon_0$: $\Phi = \oint \vec{E}\cdot d\vec{A} = \dfrac{q_{enc}}{\varepsilon_0}$. The flux depends only on the charge inside the surface, not on its shape or on outside charges — a point NEET tests directly.

Gauss's law makes short work of symmetric charge distributions. For an infinite line of charge the field is $E = \dfrac{\lambda}{2\pi\varepsilon_0 r}$ (falling as $1/r$); for an infinite charged sheet it is $E = \dfrac{\sigma}{2\varepsilon_0}$ (uniform, independent of distance); and for a charged spherical shell the field outside is that of a point charge while inside it is exactly zero. These three standard results appear again and again in NEET problems.

The electric potential at a point is the work done per unit charge in bringing a small positive test charge from infinity to that point: $V = \dfrac{W}{q}$. It is a scalar, which makes it far easier to handle than the field — potentials from several charges simply add algebraically, with sign. For a point charge, $V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$, positive for a positive charge and negative for a negative one.

Field and potential are intimately linked: the field points in the direction of decreasing potential, and for a uniform field $E = \dfrac{V}{d}$ (so the field can be expressed in $\text{V m}^{-1}$). This relation is the basis of many NEET numericals comparing field strength with the potential difference across a gap.

The potential energy of a charge $q$ at potential $V$ is $U = qV$, and for a pair of charges $U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r}$. A positive value means the configuration stores energy (like charges, which repel), while a negative value means a bound, attractive configuration. Tracking the sign of this energy is a common NEET pitfall.

A surface on which the potential is constant everywhere is an equipotential surface. No work is done in moving a charge along such a surface, and the electric field is always perpendicular to it. The surface of any conductor in equilibrium is an equipotential, and equipotentials around a point charge are concentric spheres — facts NEET often probes with assertion-reason questions.

A capacitor stores charge and energy in the electric field between two conductors. Its capacitance is the charge stored per unit potential difference, $C = \dfrac{Q}{V}$, measured in farads. For a parallel-plate capacitor in vacuum, $C = \dfrac{\varepsilon_0 A}{d}$ — capacitance grows with plate area $A$ and shrinks as the separation $d$ increases, the design lever for real capacitors.

The energy stored is $U = \dfrac{1}{2}CV^{2} = \dfrac{1}{2}QV = \dfrac{Q^{2}}{2C}$. Choosing the right form for a given problem — whether $V$ or $Q$ is held constant — is a recurring NEET skill, because connecting a capacitor to a battery fixes $V$, while isolating a charged capacitor fixes $Q$.

Capacitors combine in two ways. In series the charge is the same on each and the reciprocals add: $\dfrac{1}{C_s} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dots$, giving a smaller net capacitance. In parallel the voltage is the same and capacitances simply add: $C_p = C_1 + C_2 + \dots$. Note this is the opposite of how resistors behave, a comparison NEET enjoys testing.

Inserting a dielectric (an insulator) between the plates increases the capacitance by a factor equal to its dielectric constant $K$: $C = \dfrac{K\varepsilon_0 A}{d}$. The dielectric becomes polarised, partly cancelling the field, which lets the capacitor hold more charge at the same voltage. If the capacitor stays connected to a battery the charge rises; if it is isolated the voltage falls instead — a distinction worth memorising for exam numericals.