Bihar Board - Class 12 Physics - Chapter 2: Electric Potential and Capacitance Handwritten Notes

Electric potential and capacitance are key concepts in electrostatics that describe energy and charge storage in electrical systems. Electric potential refers to the work done to move a charge in an electric field, while capacitance is the ability of a system to store electric charge. These principles are fundamental for understanding energy distribution and storage in circuits and devices like capacitors.

Key Points

1. Electric Potential ($V$)

   • Definition: The work done per unit charge in bringing a test charge from infinity to a point in an electric field.
     $V = \frac{W}{q}$
   • Unit: Volt (V).
   • Relation with Electric Field:
     The electric field is the negative gradient of potential:
     $\vec{E} = -\nabla V$
   • Potential due to a point charge:
     $V = k \frac{q}{r}$

2. Potential Energy of a System of Charges

   • The potential energy of two charges $q_1$ and $q_2$ separated by distance $r$:
     $U = k \frac{q_1 q_2}{r}$
   • For a system of charges, total potential energy is the sum of individual interactions.

3. Equipotential Surfaces

   • Surfaces where the electric potential is constant.
   • No work is done in moving a charge along an equipotential surface.
   • Equipotential surfaces are perpendicular to electric field lines.

4. Capacitance ($C$)

   • Definition: The ability of a system to store electric charge per unit potential difference.
     $C = \frac{Q}{V}$
   • Unit: Farad (F).

5. Capacitors

   • Parallel Plate Capacitor:
     Capacitance is given by:
     $C = \frac{\epsilon_0 A}{d}$
     where $A$ is the plate area, $d$ is the separation, and $\epsilon_0$ is the permittivity of free space.
   • Energy Stored in a Capacitor:
     $U = \frac{1}{2} C V^2$
   • Dielectric increases the capacitance by reducing the electric field:
     $C' = kC$
     where $k$ is the dielectric constant.

6. Combination of Capacitors

   • Series Combination:
     $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$
   • Parallel Combination:
     $C_{\text{eq}} = C_1 + C_2 + \dots$

7. Applications

   • Capacitors are used in energy storage, filtering, and timing circuits in electronic devices.
   • Electric potential and capacitance principles are essential in designing efficient power systems and electronic components.

Conclusion

Electric potential and capacitance are vital concepts that govern the behavior of charges and energy in electrostatic systems. Understanding these concepts is crucial for advancements in electronics, energy storage, and circuit design.

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