Class 12 Physics · NCERT notes for NEET

Electrostatic Potential and Capacitance: NCERT Notes, Formulas and Tricks for NEET

Potential, equipotentials, potential energy, conductors, dielectrics and capacitors. NEET asks a few questions from this chapter almost every year, most often on capacitor combinations, the effect of a dielectric and stored energy.

• 1. Electric potential
• 2. Equipotential surfaces and E-V relation 🔒
• 3. Potential energy of a system of charges 🔒
• 4. Electrostatics of conductors 🔒
• 5. Dielectrics and polarisation 🔒
• 6. Capacitors and the parallel plate capacitor 🔒
• 7. Capacitors in series and parallel 🔒
• 8. Energy stored in a capacitor 🔒

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Open the interactive version (simulations and tap-to-answer quick checks).

Topic 1

Electric potential

A bird sits safely on an 11 kV line: it touches only one wire, so there is no potential DIFFERENCE across its body. Potential, not field, decides who gets a shock.

• The electrostatic force is conservative, so the work done in moving a charge slowly (no acceleration) depends only on the start and end points, not on the path.
• Potential at a point $=$ work done by an external agent to bring a unit positive charge from infinity to that point without acceleration. It is a scalar; $1\text{V}=1\text{J/C}$.
• Potential difference: $V_B-V_A=\frac{W_{AB}}{q}=-{\int }_A^B\vec{E}\cdot d\vec{l}$.
• Point charge: $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$ with $V=0$ at infinity. Positive for $+q$, negative for $-q$, falls as $1/r$ (slower than $E\propto 1/r^2$).
• Short dipole ($r\gg a$): $V=\frac{1}{4\pi {\epsilon }_0}\frac{p\cos \theta }{r^2}$. Largest on the axis, zero on the whole equatorial plane, falls as $1/r^2$.
• A dipole's potential depends on both $r$ and $\theta$ (angle between $\vec{r}$ and $\vec{p}$); a point charge's potential depends only on $r$.
• Many charges: add the potentials as scalars with their signs, $V=\frac{1}{4\pi {\epsilon }_0}\sum \frac{q_i}{r_i}$.
• Thin shell of radius $R$: outside $V=\frac{q}{4\pi {\epsilon }_{0}r}$; on the surface and everywhere inside $V=\frac{q}{4\pi {\epsilon }_{0}R}$, a constant (because $E=0$ inside).
• $E=0$ does not imply $V=0$, and $V=0$ does not imply $E=0$. Midway between $+q$ and $-q$: $V=0$ but $E\ne 0$.

Formulas

• $V=\frac{W}{q}$
  Potential (or potential difference) in volts, $1\text{V}=1\text{J/C}$
• $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
  Point charge, $V=0$ at infinity; $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9{\text{N m}}^2{\text{C}}^{-2}$
• $V=\frac{1}{4\pi {\epsilon }_0}\frac{p\cos \theta }{r^2}$
  Short dipole; $\theta$ measured from $\vec{p}$
• $V_B-V_A=-{\int }_A^B\vec{E}\cdot d\vec{l}$
  Potential difference from the field
• $V_{\text{inside shell}}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R}$
  Same at every inside point, including the centre

Tips, tricks and hacks

Common mistakes

NEET traps

"At the centre of a charged ring/shell the field is zero, so the potential is zero": false. $V_{\text{centre}}=kQ/R$ for both.

NEET asks the number of points on the line of two unlike charges where $V=0$ (two: one between, one outside near the smaller charge) and where $E=0$ (one, outside near the smaller charge).

Work done in moving a charge between two points of equal potential is zero, whatever the path, even through a strong field.

Practise Electrostatic Potential and Capacitance questions

Topic-wise practice from Level 1 to Level 3, NCERT-based questions and NEET PYQs, with a full solution after every answer.