CBSE Class 12 Physics Notes Chapter 2 Electrostatic Potential and Capacitance

In our technologically driven world, the principles of Electrostatic Potential and Capacitance find multiple applications that impact our daily lives. The touchscreens of our smartphones and even the power storage in electric vehicles operate on concepts of electrostatic potential and capacitance. Imagine your phone's battery, acting as a capacitor, storing electrical energy for efficient usage. 

• Electrostatic potential is the amount of work done per unit positive charge in moving it from infinity to a point in an electric field. 
• Capacitance is the ability of a system to store electric charge. 
• It depends on the shape, size, and separation of conductors and plays a vital role in various electronic applications.

CBSE Class 12 Physics Chapter 2 delves into essential concepts like electric charges, electric potential, capacitance, dielectric behavior, conductors, insulators, and parallel plate capacitors. These comprehensive notes of Chapter 2 Electrostatic Potential and Capacitance provide a thorough understanding of the principles governing electric charges for CBSE 12th-class Physics students.

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Class 12 Physics Chapter 2 Notes - Electrostatic Potential and Capacitance

Electrostatic Potential

• The electrostatic potential at any point in an electric field is the work done per unit positive test charge in bringing it from infinity to that point against the electrostatic force.
• Formula: V = W/q

where,

• V is the potential,
• W is the work done, and
• Q is the charge.

• SI Unit: The SI unit of electrostatic potential is the volt (V).
• CGS Unit: Stat Volt
• Dimensional Formula: [M L² T^-3 A^-1]

Electrostatic Potential

Electrostatic force 

The electric force produced by the electric charges at rest is known as Electrostatic force. It is conservative.

According to Colulomb’s law, the electrostatic force is given by

F = k Q₁Q₂/r²

• Work done in moving a charge between points depends only on those points, not the path taken.
• Work done by an external force equals the difference in potential energy (q*(V_P – V_R)) between the final and initial points.
• Potential is work per unit charge to bring a charge from infinity to that point.

Potential Due to a Point Charge

• Potential at a point is the work done per unit charge bringing a test charge from infinity to that point. 
• It shows the potential energy a charge has at that location.
• Formula: V(r) = k * Q / r, where:

• V(r) is the potential at a distance r from the point charge.
• k is Coulomb's constant (a unit conversion factor).
• Q is the magnitude of the point charge.

• V(r) will be positive if Q is positive, and it is negative if Q is negative.
• Potential decreases with increasing distance from the point charge (inversely proportional).

Potential Due to a Point Charge

Potential Due to an Electric Dipole

• The electric potential at a point in space due to an electric dipole is the work done per unit positive charge in bringing a positive test charge from infinity to that point.
• Formula: V(r, θ) = k * p cos(θ) / r² (where p is the dipole moment, θ is the angle between the point and the dipole axis, and r is the distance from the origin).
  • On the dipole axis (θ = 0°): V = ± kp/r² (depending on which side of the dipole).
  • On the equatorial plane (θ = 90°): V = 0 (potential cancels out from both charges).
• The potential decreases as you move away from the dipole along its axial line.
• It follows an inverse square relationship with the distance from the dipole.

Potential Due to an Electric Dipole

Potential Due to a System of Charges

• Superposition Principle: The potential at a point due to a system of charges is the algebraic sum of the potentials created by each charge at that point.
• Formula: V = k * Σ (Q_i / r_i), where:
  • V is the total potential at the point.
  • k is Coulomb's constant.
  • Q_i is the magnitude of the i^th charge.
  • r_i is the distance from the i^th charge to the point.

Equipotential Surfaces

• Surfaces where the electric potential is constant are called equipotential surfaces.
• No work is done moving a charge along the surface, as the field doesn't exert any force in that direction.

Equipotential Surfaces

Relation between Electric Field and Potential

The relationship between the electric field (E) and electric potential (V) is expressed by the formula:

E = − dV/dx

Here, dx is the infinitesimal displacement along the direction of the electric field. 

This formula highlights that the electric field points in the direction of the steepest decrease in electric potential.

Relation between Electric Field and Potential

Potential Energy of a System of Charges

• The potential energy (U) of a system of charges is the work done in assembling the charges from infinity to their respective positions in the system.
• For a system of charges q₁, q₂, …., q_n at positions r₁, r₂, …, r_n, the potential energy (U) is given by the superposition principle:

U = Σⁿ_i=1 Σⁿ_j=i+1 k.q_iq_j/r_ij

k = Coulomb’s constant, q_i and q_j are charges, r_ij is the separation between charges i and j.

Potential Energy of a System of Charges

Potential Energy in an External Field

• Work done in bringing a charge from infinity to a point
• Formula: U = qV(r), where:
  • U is the potential energy of the charge.
  • q is the charge magnitude.
  • V(r) is the external potential at the charge's location (depends on both field and position).

Electrostatics of Conductors

• Inside a conductor, the electrostatic field is zero.
• Electrostatic potential is constant throughout the volume of the conductor.

Dielectrics and Polarization

• Dielectrics are non-conducting substances.
• Polar and non-polar molecules exhibit different behaviours in an external electric field.
• Polarization in dielectrics leads to induced surface charge density.

Dielectrics and Polarization

Capacitors and Capacitance

• A capacitor consists of two conductors separated by an insulator.
• Capacitance (C) is the ratio of charge (Q) to potential (V).

Parallel Plate Capacitor

• A parallel plate capacitor is a device that stores electric charge by creating a uniform electric field between two parallel conductive plates separated by a dielectric material.

• Formula: C = εA/d, where:
  • C is the capacitance (ability to store charge).
  • ε is the permittivity of the dielectric material.
  • A is the area of each plate.
  • d is the distance between the plates.
• Capacitance increases:
  • with a larger plate area (more charge can be stored).
  • with a thinner dielectric (stronger field for a given voltage).
  • with a higher permittivity dielectric (more effective charge separation).

Parallel Plate Capacitor

Effect of Dielectric on Capacitance

• When a dielectric is introduced between capacitor plates, it polarizes, creating induced dipoles that oppose the electric field.
• The presence of a dielectric increases the capacitance (C = K⋅C₀), where K is the dielectric constant.

Combination of Capacitors

• Series Combination: In series, the reciprocal of the total capacitance (C_total) = is the sum of reciprocals of individual capacitances.

1/C_total = 1/C₁ + 1/C₂ + 1/C₃ + … 1/C_n

• Parallel Combination: In parallel, the total capacitance is the sum of individual capacitances.

C_total = C₁ + C₂ + C₃ + … C_n

Combination of Capacitors

Energy stored in capacitor

Formula: The energy (U) stored in a capacitor is given by 

•  U = 1/2 CV²
• U = 1/2 QV
• U = 1/2 (Q²/C)

Where 

• C is the capacitance
• V is the potential difference across the capacitor
• Q is th charge stored in the capacitor

The energy is stored in the electric field between the capacitor plates when a voltage is applied and is released when the capacitor discharges.

Energy stored in capacitor

There are Some important List Of Top Physics Questions On Electrostatic Potential And Capacitance Asked In CBSE CLASS XII

The CBSE Class 12 Physics Exam, Unit-I, Electrostatics, includes Chapter 1 (Electric Charges and Fields) and Chapter 2 (Electrostatic Potential and Capacitance). Unit II delves into Current Electricity with Chapter 3. Overall these 3 chapters collectively have a weightage of 16 marks in the final Class 12th Physics examination.

Electrostatic Potential and Capacitance