Edunes Online Education
BOARD: CBSE and AHSEC (ASSAM)
CLASS 11 | Physics | Electric Potential and Capacitance
Important Questions and Answers
Short Answer Type (1-2 Marks)
- Define electric potential at a point. What is its SI unit?
- Define potential difference between two points.
- Define electrostatic potential energy.
- What is an equipotential surface? Give an example.
- What is the relation between electric field and electric potential?
- Can two equipotential surfaces intersect each other? Justify your answer.
- Why is the electric field zero inside a conductor?
- Write an expression for the capacitance of a parallel plate capacitor.
- What is a dielectric constant? How does it affect the capacitance of a capacitor?
- Define farad. How is it related to other units of capacitance?
Short Answer Type (1–2 Marks) — Answers
1. Define electric potential at a point. What is its SI unit?
Electric potential at a point is the work done per unit positive charge in bringing a test charge from infinity to that point without acceleration.
\( V = \dfrac{W}{q} \)
SI unit: Volt (V)
\( 1 V = 1 JC^{-1} \)
2. Define potential difference between two points.
Potential difference between two points is the work done per unit charge in moving a positive test charge from one point to another in an electric field.
\( V_B - V_A = \dfrac{W}{q} \)
3. Define electrostatic potential energy.
Electrostatic potential energy is the work done in bringing a system of charges from infinity to their given positions against electrostatic forces.
For a charge (q) in potential (V): \( U = qV \)
4. What is an equipotential surface? Give an example.
An equipotential surface is a surface on which electric potential is the same at every point.
Example:
Surface of a charged conducting sphere
Surfaces perpendicular to uniform electric field lines
5. What is the relation between electric field and electric potential?
The electric field is the negative gradient of electric potential.
\( E = -\dfrac{dV}{dr} \) Or in vector form: \( \vec{E} = - \nabla V \)
This means the electric field points in the direction of decreasing potential.
6. Can two equipotential surfaces intersect each other? Justify your answer.
No, two equipotential surfaces cannot intersect.
Reason:
If they intersected, the point of intersection
would have two different potentials, which is physically impossible.
7. Why is the electric field zero inside a conductor?
Inside a conductor, free electrons move until electrostatic equilibrium is reached.
This rearrangement of charges cancels the internal electric field, making: E = 0
8. Write an expression for the capacitance of a parallel plate capacitor.
\( C = \dfrac{\varepsilon_0 A}{d} \)
Where
(C) = capacitance
(A) = area of plates
(d) = separation between plates
\( \varepsilon_0 \) = permittivity of free space
9. What is a dielectric constant? How does it affect the capacitance of a capacitor?
The dielectric constant (K) is the ratio of permittivity of the medium to permittivity of vacuum.
\( K = \dfrac{\varepsilon}{\varepsilon_0} \)
When a dielectric is inserted between capacitor plates:
\( C = \dfrac{K \varepsilon_0 A}{d} \)
Thus, capacitance increases by a factor of (K).
10. Define farad. How is it related to other units of capacitance?
Farad (F) is the SI unit of capacitance.
A capacitor has a capacitance of 1 farad if a charge of 1 coulomb produces a potential difference of 1 volt.
\( C = \dfrac{Q}{V} \)
\( 1 F = \dfrac{\text{1 C}}{\text{1 V}} \)
Common subunits:
1 \( \mu F = 10^{-6} F \), 1 \( nF = 10^{-9} F \) , 1 \( pF = 10^{-12} F \)
- Derive an expression for the electric potential at a point due to a point charge.
- Derive an expression for the potential energy of a system of two point charges.
- Derive an expression for the capacitance of a parallel plate capacitor with a dielectric medium.
- What is a Van de Graaff generator? Explain its principle of operation.
- Show that the work done in moving a charge between two points on an equipotential surface is zero.
- Derive an expression for the energy stored in a charged capacitor.
- A parallel plate capacitor has a plate area of 1m² and a plate separation of 1 mm. If the dielectric medium between the plates is air, find its capacitance.
- A capacitor of 5μF is charged to 10V. Calculate the energy stored in it.
- A 20μF capacitor is connected in series with a 10μF capacitor. Find the equivalent capacitance.
- Three capacitors of 4μF, 6μF, and 12μF are connected in parallel. Find the total capacitance.
- Explain the concept of electric potential due to a point charge and derive its expression.
- Derive the expression for the capacitance of a spherical capacitor.
- What is a capacitor? Explain how capacitors are connected in series and parallel and derive their equivalent capacitance formulas.
- Explain the principle and working of a Van de Graaff generator with a neat diagram.
- Derive the expression for the energy density of an electric field in a capacitor.
