Class 12th Physics Chapter-2 Notes on Electrostatic Potential

ELECTROSTATIC POTENTIAL

(Study Material & Notes )

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1. Why do we need Electrostatic Potential?

• Electrostatic force is a conservative force.

• For conservative forces, work done depends only on initial and final positions, not on the path.

• Hence, we can define:

  • Electrostatic Potential Energy

  • Electrostatic Potential

This is similar to gravitational potential energy and gravitational potential.

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2. Electrostatic Potential Energy

Definition

Electrostatic potential energy of a charge is the work done by an external force in bringing the charge from infinity to a given point in an electric field without acceleration.

Important Points

• Test charge must be very small (so it does not disturb the field).

• External force must be equal and opposite to electric force.

• Work done is stored as potential energy.

Mathematical Expression

$$\mathrm{\Delta }U=-W_{\text{electric}}$$

• Only change in potential energy is physically meaningful.

• Absolute value depends on the chosen reference point.

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3. Reference Point for Potential Energy

• Potential energy is defined up to an additive constant.

• Convenient choice:

  $$U=0\text{at infinity}$$

This choice is universally used in electrostatics.

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4. Electrostatic Potential

Definition (Most Important)

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.

Symbol

• Electrostatic potential → V

Mathematical Definition

$$V=\frac{U}{q}$$

or,

$$V_P-V_R=\frac{W_{RP}}{\mathrm{q<span\; class="vlist"\; style="font-size:\; revert;\; font-family:\; var(--wp--preset--font-family--manrope);\; letter-spacing:\; -0.1px;"><span\; class="msupsub"><span\; class="vlist-s"></span></span></span><span\; class="vlist-s"\; style="font-size:\; revert;\; font-family:\; var(--wp--preset--font-family--manrope);\; letter-spacing:\; -0.1px;"></span>}}$$

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5. Physical Meaning of Electrostatic Potential

• It represents the potential energy per unit charge.

• It tells us how much work is required to bring a charge to a point.

• Higher potential → more work needed for a positive charge.

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6. Unit of Electrostatic Potential

SI Unit: Volt (V)

$$1\text{Volt}=1\text{Joule per Coulomb}$$

$$1V=1\frac{J}{C}$$

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7. Potential Difference

Definition

Potential difference between two points is the work done per unit charge in moving a test charge from one point to another.

Expression

$$V_P-V_R=\frac{W_{RP}}{q}$$

Important Notes

• Only potential difference is measurable.

• Absolute potential has no physical meaning unless a reference is chosen.

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8. Potential at Infinity

• By convention:

  $$V(\mathrm{\infty })=0$$

• Then,

$$V=\frac{\text{Work done in bringing unit charge from infinity}}{}$$

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9. Electrostatic Potential Due to a Point Charge

Consider a point charge Q at the origin.

Expression

$$V(r)=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}$$

where:

• $r$ = distance from the charge

• ${\epsilon }_0$ = permittivity of free space

Nature of Potential

• If $Q>0$ → $V>0$

• If $Q<0$ → $V<0$

Key Difference from Electric Field

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10. Potential Due to a System of Charges

Principle Used

👉 Superposition Principle

Expression

For charges $q_1,q_2,q_3,\mathrm{.}\mathrm{.}\mathrm{.}$

$$V=\frac{1}{4\pi {\epsilon }_0}(\frac{q_1}{r_1}+\frac{q_2}{r_2}+\frac{q_3}{r_3}+\dots )$$

• Potential is a scalar, so algebraic sum is taken.

• Easier to calculate than electric field.

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11. Potential Due to a Dipole (Short Note – Pre-Equipotential)

For a dipole with moment p:

$$V=\frac{1}{4\pi {\epsilon }_0}\frac{p\cos \theta }{r^2}$$

Special Cases

• Axial line: Potential is maximum

• Equatorial plane: Potential = 0

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12. Relation Between Potential and Work

$$W=q\mathrm{\Delta }V$$

• Positive charge moves naturally from higher to lower potential.

• Negative charge moves from lower to higher potential.

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13. Important Exam Points (Very High Yield)

• Electrostatic potential is a scalar quantity

• Defined only for conservative fields

• Depends on position, not path

• Potential can be positive, negative, or zero

• Easier to calculate than electric field

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This material is directly aligned with NCERT Class 12 Physics, suitable for CBSE Board, NEET, and JEE (conceptual) preparation.