Chapter 2: Electrostatic Potential and Capacitance Short Questions | physics Class 12 CBSE

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Chapter 2: Electrostatic Potential and Capacitance Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Define electrostatic potential at a point and state its SI unit.

Electrostatic potential at a point is the work done by an external force in bringing a unit positive charge from infinity to that point, without acceleration.
It is a scalar quantity; physically significant quantity is the potential difference V_P − V_R = W_RP/q, not absolute V.
Its SI unit is volt (V), where 1 V = 1 J C⁻¹.

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Question 2

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Why is the work done by an electrostatic field in moving a charge between two points independent of the path taken?

The Coulomb force is a conservative force, analogous to the gravitational force — both have inverse-square dependence on distance.
For a conservative force, work done depends only on the initial and final positions, not the path connecting them.
This path-independence is the defining characteristic of a conservative force and is provable using Coulomb's law.

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Question 3

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Write the expression for electric potential at distance r from a point charge Q and explain the significance of the sign of Q.

The potential is V(r) = Q/(4πε₀r), derived by calculating work done in bringing a unit positive charge from infinity to point P.
For Q > 0, V > 0: positive external work is needed against repulsive force to bring the unit positive charge.
For Q < 0, V < 0: the attractive force assists the motion; the external agent receives energy (does negative work).

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Question 4

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How does the potential due to an electric dipole differ from that due to a single point charge in its dependence on distance?

Potential due to a single charge: V = Q/(4πε₀r), falls as 1/r — decreasing slowly with distance.
Potential due to a dipole: V = p cosθ/(4πε₀r²), falls as 1/r² — decreasing much faster at large distances.
Additionally, dipole potential depends on angle θ, making it non-spherically-symmetric; single-charge potential has no angular dependence.

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Question 5

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What is the value of electric potential at the equatorial point of a dipole? Justify your answer.

The electric potential at any equatorial point (θ = π/2) of a dipole is zero.
From V = p cosθ/(4πε₀r²), at θ = π/2: cos(π/2) = 0, so V = 0.
Physically, the equal distances from +q and −q at the equatorial point mean their potential contributions (+kq/r and −kq/r) exactly cancel.

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Question 6

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State the superposition principle for electrostatic potential. How does it differ from superposition for electric field?

For potential: total V at a point = algebraic (scalar) sum of potentials due to each charge: V = V₁ + V₂ + ... + Vₙ.
For electric field: total E = vector sum of fields, requiring addition of both magnitude and direction.
Since potential is scalar, its superposition is simpler — no directions needed — making calculations easier for complex charge distributions.

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Question 7

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Define an equipotential surface and state two of its important properties.

An equipotential surface is a surface on which the electrostatic potential has the same constant value at every point.
Property 1: No work is done in moving a test charge along an equipotential surface, since there is no potential difference.
Property 2: The electric field at every point is always perpendicular to the equipotential surface; any tangential field component would do work, contradicting the definition.

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Question 8

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Derive the relation between electric field E and potential V showing E = −dV/dl.

Consider equipotential surfaces A and B with potentials V and V + dV, perpendicular distance dl. Moving unit positive charge from B to A against field E does work |E|dl.
This work equals potential difference V_A − V_B = V − (V + dV) = −dV, so |E|dl = −dV.
Therefore |E| = −dV/dl; the negative sign means E points in the direction of decreasing potential.

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Question 9

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Write the expression for potential energy of two point charges q₁ and q₂. When is this energy positive and when negative?

Potential energy: U = (1/4πε₀) × q₁q₂/r₁₂, representing work done assembling the configuration from infinity.
If q₁q₂ > 0 (like charges), U > 0: positive work must be done against repulsive force to bring them to finite separation.
If q₁q₂ < 0 (unlike charges), U < 0: attractive force does positive work during assembly, releasing energy; external work is negative.

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Question 10

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What is the potential energy of an electric dipole in a uniform external field? At what orientation is it in stable equilibrium?

Potential energy at angle θ to field E: U(θ) = −pE cosθ = −p·E, with U = 0 at θ = 90°.
At θ = 0° (p parallel to E): U = −pE, the minimum value — stable equilibrium.
At θ = 180° (antiparallel): U = +pE — maximum, unstable equilibrium. A small displacement from stable position returns the dipole to alignment.

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Question 11

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State any three important electrostatic properties of a conductor in static equilibrium.

The electric field inside a conductor is zero in the static situation; free electrons redistribute until the net internal field vanishes.
Electrostatic potential is constant throughout the volume and surface of the conductor — no work is done moving a charge inside.
Excess charge resides entirely on the conductor surface; the interior is charge-free, as proved by applying Gauss's law to any internal closed surface.

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Question 12

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Explain electrostatic shielding. Give one practical application.

Electrostatic shielding: any charge-free cavity inside a conductor has E = 0 regardless of external fields. The conductor completely shields its interior cavity from outside electrical influence.
This occurs because E = 0 inside the conductor body, so no field can penetrate to the cavity; the inner surface has no induced charges when the cavity is charge-free.
Practical application: sensitive electronic instruments are enclosed in metallic casings (Faraday cages) to protect them from external electric field interference.

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Question 13

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Distinguish between polar and non-polar molecules with one example each.

Non-polar molecule: centres of positive and negative charges coincide — no permanent dipole moment. Example: H₂, O₂, CO₂.
Polar molecule: centres of positive and negative charges are permanently separated — has a permanent dipole moment. Example: HCl, H₂O.
In an external field: non-polar molecules develop induced dipole moments; polar molecules partially align their existing permanent dipoles with the field.

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Chapter 2: Electrostatic Potential and Capacitance | Short Questions

Define electrostatic potential at a point and state its SI unit.

Why is the work done by an electrostatic field in moving a charge between two points independent of the path taken?

Write the expression for electric potential at distance r from a point charge Q and explain the significance of the sign of Q.

How does the potential due to an electric dipole differ from that due to a single point charge in its dependence on distance?

What is the value of electric potential at the equatorial point of a dipole? Justify your answer.

State the superposition principle for electrostatic potential. How does it differ from superposition for electric field?

Define an equipotential surface and state two of its important properties.

Derive the relation between electric field E and potential V showing E = −dV/dl.

Write the expression for potential energy of two point charges q₁ and q₂. When is this energy positive and when negative?

What is the potential energy of an electric dipole in a uniform external field? At what orientation is it in stable equilibrium?

State any three important electrostatic properties of a conductor in static equilibrium.

Explain electrostatic shielding. Give one practical application.

Distinguish between polar and non-polar molecules with one example each.

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