Electrostatic Potential and Capacitance

34 solved questions from Class 12 Physics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the fundamental law or governing principle of 'Electrostatic Potential and Capacitance' in Class 12 Physics? medium MCQ Fundamental Physical Law
• 2 What is the SI unit and dimensional formula for the key physical quantity studied in 'Electrostatic Potential and Capacitance'? medium MCQ SI Units & Dimensional Analysis
• 3 How does the field or potential intensity vary with distance r in 'Electrostatic Potential and Capacitance'? medium MCQ Spatial Distance Dependence
• 4 What is the net flux or circulation integral through a closed surface in 'Electrostatic Potential and Capacitance'? medium MCQ Gauss's Theorem & Boundary Integrals
• 5 Why do field lines in 'Electrostatic Potential and Capacitance' never intersect each other? medium MCQ Field Line Properties
• 6 A solid non‑conducting sphere of radius R=5 cm carries a uniform volume charge density ρ = 8×10^-8 C m^-3. Derive an expression for the total electrostatic energy stored in the sphere and evaluate its numerical value (in joules). hard 5 marks Energy of uniformly charged sphere
• 7 Three capacitors C_1=2 μF, C_2=3 μF and C_3=6 μF are connected as shown: C_1 is in series with the parallel combination of C_2 and C_3. Find the equivalent capacitance of the whole network. medium 2 marks Combination of capacitors
• 8 Two point charges are placed on the x‑axis. A charge +3 μC is at the origin and a charge -2 μC is at x = 0.20 m. Calculate the electric potential at the point P located at x = 0.50 m on the same axis. Take the potential to be zero at infinity. (Use k = 9×10^9 N m^2C^-2.) easy 2 marks Potential of point charges
• 9 A parallel‑plate capacitor of plate area A= 2.0 dm^2 and plate separation d=1.0 mm is filled with a dielectric slab of dielectric constant κ=5 that occupies only half the volume between the plates (the slab is placed so that it completely covers one half of the plate area). What is the effective capacitance of the arrangement? medium MCQ 3 marks Capacitance with partial dielectric
• 10 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=4 cm and carries a charge +Q, the outer shell has radius R_2=10 cm and carries charge -Q. (a) Derive the expression for its capacitance C. (b) If Q=2 μC, find the energy stored in the capacitor. Use ε_0 = 8.85×10^-12 F m^-1. hard 4 marks Capacitance and energy of spherical capacitor
• 11 Two equal and opposite point charges, +q at x=-a and -q at x=+a, form an electric dipole. What is the electric potential at a point on the x‑axis at x = 3a? (Take potential zero at infinity.) medium MCQ 3 marks Potential of an electric dipole on its axis
• 12 A point charge of magnitude +5 μC is placed at the origin. Calculate the electric potential at a point P located 15 cm away from the charge. Take the potential to be zero at infinity. Use k = 9×10^9 N m^2C^-2. easy 2 marks Potential of a point charge
• 13 A parallel‑plate capacitor of plate area A=30 cm^2 and separation d=2 mm is filled with two dielectric layers placed one over the other across the separation. The layer next to the positive plate has thickness d_1=0.8 mm and dielectric constant κ_1=2, while the remaining thickness d_2=1.2 mm has dielectric constant κ_2=5. Determine the effective capacitance of the arrangement. Use ε_0 = 8.85×10^-12 F m^-1. medium 3 marks Capacitance with layered dielectrics (series combination)
• 14 Capacitors C_1=4 μF and C_2=6 μF are connected in series. This series combination is then connected in parallel with a capacitor C_3=5 μF. Find the equivalent capacitance of the whole network. medium 2 marks Series‑parallel combination of capacitors
• 15 Calculate the electric potential at a point P located 8 cm from a point charge of +2 μC placed at the origin. Take the potential to be zero at infinity. Use k = 9×10^9 N m^2C^-2. easy 1 mark Potential of a point charge
• 16 A parallel‑plate capacitor has plate area A=50 cm^2 and plate separation d=1.0 mm. A dielectric slab of dielectric constant κ=4 fills the lower half of the separation (thickness d/2) while the upper half is air. Determine the effective capacitance of the arrangement. Use ε_0=8.85×10^-12 F m^-1. hard 3 marks Series combination of dielectrics in a capacitor
• 17 A parallel‑plate capacitor has plate area A=40 cm^2 and plate separation d=0.5 mm. The space between the plates is filled with two dielectric slabs placed side by side, each occupying half the plate area. The slab on the left has dielectric constant κ_1=2, and the slab on the right has dielectric constant κ_2=6. Find the effective capacitance of the arrangement. Use ε_0=8.85×10^-12 F m^-1. medium 2 marks Capacitor with mixed dielectrics (parallel arrangement)
• 18 A point charge of magnitude +3 μC is placed at the origin. Calculate the electric potential at a point P located 12 cm from the charge. Take the potential to be zero at infinity. Use k = 9×10^9 N m^2C^-2. easy 1 mark Potential of a point charge
• 19 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=5 cm and the outer shell has radius R_2=15 cm. (a) Derive the expression for its capacitance C. (b) If the capacitor is charged to a potential difference V=200 V, find the energy stored in it. Use ε_0=8.85×10^-12 F m^-1. hard 4 marks Spherical capacitor capacitance and energy
• 20 A point charge of magnitude +4,μC is placed at the origin. Calculate the electric potential at a point P located 10,cm from the charge. Take the potential to be zero at infinity. Use k=9×10^9,N m^2C^-2. easy 1 mark Electric potential of a point charge
• 21 A parallel‑plate capacitor has plate area A=60,cm^2 and plate separation d=1,mm. The space between the plates is filled with two dielectric slabs placed side by side, each occupying half the plate area. The slab on the left has dielectric constant κ_1=3, and the slab on the right has dielectric constant κ_2=5. What is the effective capacitance of the arrangement? Use ε_0=8.85×10^-12,F m^-1. medium MCQ 2 marks Capacitance of composite dielectrics
• 22 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=3,cm, the outer shell has radius R_2=12,cm, and the space between them is filled with a dielectric of relative permittivity κ=2. (a) Find the capacitance of the capacitor. (b) If the capacitor is charged to a potential difference of 150,V, calculate the energy stored in it. Use ε_0=8.85×10^-12,F m^-1. hard 3 marks Capacitance and energy of spherical capacitor
• 23 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=2,cm and the outer shell has radius R_2=8,cm, and the space between them is filled with a dielectric of relative permittivity κ=3. (a) Find the capacitance of the capacitor. (b) If the capacitor is charged to a potential difference of 250,V, calculate the energy stored in it. Use ε_0=8.85×10^-12,F m^-1. hard 4 marks Spherical capacitor with dielectric
• 24 A point charge of magnitude +3,μC is placed at the origin. Calculate the electric potential at a point P located 15,cm from the charge. Take the potential to be zero at infinity. Use k = 9×10^9,N m^2C^-2. easy 2 marks Point charge electric potential
• 25 In a network of capacitors, a 5,μF capacitor is connected in series with the parallel combination of a 3,μF and a 7,μF capacitor. The resulting combination is then connected in parallel with a 4,μF capacitor. What is the equivalent capacitance of the whole network? medium 2 marks Capacitor network equivalent capacitance
• 26 A parallel‑plate capacitor has plate area A=70,cm^2 and plate separation d=2,mm. The space between the plates is filled with two dielectric slabs placed side by side, each occupying half the plate area. The slab on the left has dielectric constant k_1=4, and the slab on the right has dielectric constant k_2=6. What is the effective capacitance of the arrangement? Use ,ε_0=8.85×10^-12,F m^-1. medium 3 marks Capacitance of parallel‑plate with side‑by‑side dielectrics
• 27 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=4,cm and the outer shell has radius R_2=12,cm. The space between the shells is filled with a dielectric of relative permittivity k=2. (a) Derive the expression for its capacitance. (b) If the capacitor is charged to a potential difference of 300,V, calculate the energy stored in it. Use ε_0=8.85×10^-12,F m^-1. hard 4 marks Spherical capacitor with dielectric
• 28 A network of capacitors consists of a 10,μF capacitor in parallel with a series combination of 6,μF and 4,μF capacitors. This overall combination is then connected in series with an 8,μF capacitor. Find the equivalent capacitance of the whole network. medium 3 marks Capacitor network analysis
• 29 A parallel‑plate capacitor has plate area A=80,cm^2 and plate separation d=2,mm. The space between the plates is filled with two dielectric slabs placed one over the other. The top slab has thickness 0.6,mm and dielectric constant k_1=3, the bottom slab has thickness 1.4,mm and dielectric constant k_2=5. What is the effective capacitance of the capacitor? Use ε_0=8.85×10^-12,F m^-1. medium MCQ 2 marks Capacitance of series dielectrics
• 30 A point charge of magnitude +5,μC is placed at the origin. Calculate the electric potential at a point P located 12,cm from the charge. Take the potential to be zero at infinity. Use k=9×10^9,N m^2C^-2. easy 1 mark Potential of a point charge
• 31 Three capacitors C_1=2 μF, C_2=3 μF and C_3=6 μF are connected as follows: C_1 is in series with the parallel combination of C_2 and C_3. Find the equivalent capacitance of the whole network. medium 3 marks Combination of series and parallel capacitors
• 32 A parallel‑plate capacitor has plate area A=80 cm^2 and plate separation d=1 mm. The space between the plates is filled with two dielectric slabs placed side by side, each occupying half the plate area. The left slab has dielectric constant κ_1=3 and the right slab has dielectric constant κ_2=5. What is the effective capacitance of the arrangement? Use ε_0=8.85×10^-12 F m^-1. medium MCQ 3 marks Capacitance with dielectrics (parallel arrangement)
• 33 A spherical capacitor consists of two concentric conducting shells. The inner shell has radius R_1=5 cm and the outer shell has radius R_2=15 cm. The space between the shells is filled with a dielectric of relative permittivity κ=2. (a) Derive the expression for its capacitance. (b) If the capacitor is charged to a potential difference of 200 V, calculate the energy stored in it. Use ε_0=8.85×10^-12 F m^-1. hard 5 marks Spherical capacitor with dielectric
• 34 A point charge of magnitude +2 μC is placed at the origin. Calculate the electric potential at a point P located 20 cm from the charge. Take the potential to be zero at infinity. Use k = 9×10^9 N m^2C^-2. easy 2 marks Potential of a point charge