Electrostatic Potential and Capacitance

part 1

Electric Potential

• Electric potential — concept and definition
• Potential difference
• Electric potential due to a point charge
• Electric potential due to a dipole
• Equipotential surfaces

part 2

Potential Energy and Conductors

• Potential energy of a system of charges
• Potential energy in an external field
• Electrostatics of conductors
• Dielectrics and polarisation
• Electric field and potential relationship

part 3

Capacitance and Capacitors

• Capacitors and capacitance
• Parallel plate capacitor
• Effect of dielectric on capacitance
• Combination of capacitors (series and parallel)
• Energy stored in a capacitor
• Van de Graaff generator

Capacitance definition

$C = \frac{Q}{V}$

★ board favourite

Parallel plate capacitor

$C = \frac{\varepsilon_0 A}{d}$

★ board favourite

Capacitors in series

$\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$

★ board favourite

Capacitors in parallel

$C = C_1 + C_2 + C_3$

★ board favourite

Energy stored in capacitor

$U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{QV}{2}$

★ board favourite

Electric potential due to point charge

$V = \frac{kq}{r}$

★ frequently asked

E and V relation

$E = -\frac{dV}{dr}$

★ frequently asked

PE of system of two charges

$U = \frac{kq_1 q_2}{r}$

★ frequently asked

PE of dipole in external field

$U = -pE\cos\theta = -\vec{p}\cdot\vec{E}$

★ frequently asked

With dielectric slab (thickness t)

$C = \frac{\varepsilon_0 A}{d - t + t/K}$

★ frequently asked

Derive an expression for the capacitance of a parallel plate capacitor with a dielectric slab of thickness t (t < d) inserted between its plates. What happens to the capacitance when the slab fills the entire gap?

Derive an expression for the electric potential at a point on the axial line of an electric dipole. Why is the potential zero at any point on the equatorial line?

A parallel plate capacitor of capacitance C is charged to potential V. The charging battery is then disconnected. If the plates are pulled apart to double the separation, what happens to (a) capacitance, (b) charge, (c) energy stored?

Derive an expression for the energy stored in a charged capacitor. A capacitor of 200 pF is charged to 300 V. It is then connected to an uncharged 100 pF capacitor. Find the common potential and the loss of energy in the process.

Three capacitors of capacitances C₁, C₂, C₃ are connected in series. Derive the formula for equivalent capacitance. If C₁=2μF, C₂=3μF, C₃=6μF are connected in parallel across a 100V battery, find the charge on each and total energy stored.

Derive an expression for the electric potential at a point due to a point charge Q. Draw the variation of potential V and field E with distance r from the charge.

Why is the electric field always perpendicular to an equipotential surface?

Derive an expression for the potential energy of a system of two point charges q₁ and q₂ separated by a distance r in the absence of an external field.

Explain why the energy stored in a capacitor increases when a dielectric slab is inserted between the plates while the battery remains connected.

Draw the equipotential surfaces for a single positive point charge. What is the work done in moving a charge along an equipotential surface?

Two capacitors of capacitance 6 μF and 12 μF are connected in series with a 12 V battery. Find (a) the equivalent capacitance, (b) the charge on each capacitor, and (c) the potential difference across each.

Define dielectric constant of a medium in terms of capacitance.

How many marks is Electrostatic Potential and Capacitance worth in the Class 12 board exam?

Around 5 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. Energy stored in capacitors is a favourite numeric.

Is Electrostatic Potential and Capacitance easy or hard?

It's rated hard — one of the tougher chapters in Class 12 Physics. Most students need about 5 hours to cover it well.

What are the important topics in Electrostatic Potential and Capacitance?

The chapter covers 13 NCERT topics in 3 areas: Electric Potential; Potential Energy and Conductors; Capacitance and Capacitors.

What questions come from Electrostatic Potential and Capacitance in board exams?

Between 2018–2024, CBSE board papers asked questions from this chapter on Parallel Plate Capacitor, Potential due to Dipole, Capacitors, Energy of Capacitors — 1- to 5-mark questions.