Capacitors — Parallel plate, spherical, cylindrical
Electrostatics
18
JEE Qs
8%
Hard
75
min
Thoroughly understand the derivations of capacitance for all geometries as they solidify understanding of electric fields, potentials, and charge distribution, which are key for solving complex problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1Capacitance is a geometric property of a conductor system and the dielectric medium between them; it does not depend on the charge Q or potential difference V.
- 2The electric field inside an ideal parallel plate capacitor is uniform and perpendicular to the plates (ignoring fringe effects).
- 3Energy stored in a capacitor resides in the electric field established between its plates.
- 4Derivations for spherical and cylindrical capacitors involve using Gauss's Law to find the electric field, then integrating E.dl to find the potential difference.
- 5Introducing a dielectric material between capacitor plates increases the capacitance by a factor of K (dielectric constant) and decreases the electric field and potential difference for a given charge.
⚠️ Common Mistakes
- ✕Confusing the potential 'V' at a point with the potential difference 'V' across the capacitor, which is crucial for C = Q/V.
- ✕Incorrectly applying radii in spherical and cylindrical capacitor formulas (e.g., swapping R1 and R2 or using R2-R1 vs R1-R2 without adjusting sign).
- ✕Forgetting the factor of 1/2 in energy formulas (U = 1/2CV²).
- ✕Calculating the force between capacitor plates using F = QE, where E is the total field, instead of the field due to one plate acting on the other.
📝 Practice Questions
See allQ38.A capacitor, C1 = 6μ F is charged to a potential difference of V0 = 5 V using a 5 V battery. The battery is removed and another capacitor, C2 = 12μ F is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the 2025 (29 Jan Shift 2) JEE Main Previous Year Paper charges (q1 and q2) on the capacitors C1 and C2 when equilibrium condition is reached. (1) q1 = 10μC, q2 = 20μC (2) q1 = 30μC, q2 = 15μC (3) q1 = 20μC, q2 = 10μC (4) q1 = 15μC, q2 = 30μC
Q44.A point charge causes an electric flux of −2 × 104Nm2C−1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given ϵ0 = 8.85 × 10−12C2 N−1 m−2 ) (1) 15.7 × 10−8C (2) 17.7 × 10−8C (3) −15.7 × 10−8C (4) −17.7 × 10−8C
Q45.An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σo . Choose the correct option from the following. (1) Potential energy and torque both are maximum. (2) Torque on dipole is zero and net force is directed away from the sheet. (3) Torque on dipole is zero and net force acts (4) Potential energy of dipole is minimum and torque towards the sheet. is zero.
Q26.An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s. If the magnitude of the electric field between the plates is 9.1 V/cm , then the vertical component of velocity of electron is (mass of electron = 9.1 × 10−31 kg and charge of electron = 1.6 × 10−19C ) (1) 0 (2) 1 × 106 m/s (3) 16 × 106 m/s (4) 16 × 104 m/s
Q38.A line charge of length ' a ' is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' 2 a ' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be . (Take, ϵ0 as the free space permittivity) (1) λa (2) λa 2ϵ0 4ϵ0 (3) λa (4) λa 16ϵ0 8ϵ0
Q44.A parallel-plate capacitor of capacitance 40μ F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are (1) 4 mC and 0.2 J (2) 8 mC and 2.0 J (3) 2 mC and 0.4 J (4) 2 mC and 0.2 J 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
NCERT Chapters
- Class 12 Physics Ch 2: Electrostatic Potential and Capacitance