Electric Potential — Due to point charge, shell, dipole
Electrostatics
18
JEE Qs
8%
Hard
75
min
Master the scalar nature of electric potential and its direct relation to the electric field through E = -∇V for efficient problem solving.
🧮 Key Formulas
✅ Key Points for JEE
- 1Electric potential is a scalar quantity, making calculations simpler via direct algebraic summation, unlike electric field which requires vector addition.
- 2The reference point for potential (usually V=0 at infinity) is crucial; ensure consistency when comparing potentials.
- 3The potential inside a conductor (and thus inside a uniformly charged spherical shell) is constant and equal to its surface potential.
- 4Electric potential due to a dipole falls off as 1/r^2, which is a faster rate than the 1/r dependence for a single point charge.
- 5The relationship E = -∇V (or E = -dV/dr in 1D) is fundamental for interconverting between electric potential and electric field.
⚠️ Common Mistakes
- ✕Forgetting to include the sign of the charge when calculating electric potential, as potential is a signed scalar quantity.
- ✕Confusing electric potential with electric potential energy; potential is energy per unit charge, while potential energy is for a specific charge or system.
- ✕Incorrectly applying the distance dependence (1/r for point charge, 1/r^2 for dipole, constant inside shell) in different scenarios.
- ✕Not understanding that while the electric field inside a charged spherical shell is zero, the electric potential inside is constant and non-zero.
📝 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 Part 1 Ch 2: Electrostatic Potential and Capacitance