Class 12 Physics, Chapter 2 (NCERT). 15 questions by concept, 2 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
An isolated point charge has potential V0 at distance r, with zero at infinity. What is its potential at distance 2r?
(c) V0/2
Point-charge potential is kQ/r. Only the first power of distance enters.
Charges +5q at x=0 and -3q at x=16 cm have zero potential at infinity. A student solves only 0<x<16 cm and concludes that x=10 cm is the only finite zero. Which correction is needed?
(a) Keep x=10 cm and add the exterior root x=40 cm
For x>16cm, 5/x=3/(x-16) gives x=40cm. This satisfies the exterior interval and must be included.
A 12pF capacitor is charged to 100V. How much energy is stored?
(a) 60000 pJ
Use U=CV²/2. At 50V this is 15000pJ=1.5×10^-8J, matching the textbook anchor.
The same test charge is moved between the same two points in a static electric field along paths of lengths L and 3L. Which comparison of electric-field work is correct?
(b) The two works are equal because the endpoint potential difference is the same
Electrostatic work is -q(V_final-V_initial). The route and its length do not change this difference.
An 18pF air capacitor stays connected to a 100V ideal battery while a dielectric K=6 completely fills its gap. How much ADDITIONAL charge flows onto its positive plate?
(c) 9000 pC
The battery fixes voltage. Initial charge is 1800pC; final charge is K times that, so the additional charge is(K-1)×1800pC.
Two parallel equipotential lines are shown in cross-section. The potential varies linearly between them. In which horizontal direction does the electric field point?
(a) To the left
The electric field is normal to the lines and points from higher potential to lower potential.
Equal charges +q and -q form a dipole. At a finite point on its equatorial plane, what are the potential and field? Use zero potential at infinity.
(a) Potential is zero; field is nonzero and normal to the plane
Equal distances cancel scalar potentials. The charge fields have components that add opposite to the dipole moment, normal to the equatorial plane.
A permanent dipole has zero torque when parallel or antiparallel to a uniform electric field. Which classification is correct?
(c) Parallel is stable; antiparallel is unstable
U=-pEcosθ has its minimum at 0° and maximum at 180°. Stability concerns a small displacement from the zero-torque orientation.
An isolated conductor is in electrostatic equilibrium at a measured surface potential +120V relative to infinity. Which statement about its material interior is correct?
(c) E=0 and V=+120V
Zero field makes potential constant throughout the conductor; it does not set the constant to zero.
An ordinary dielectric has a finite permittivity. Why does it generally keep a nonzero field inside it when the external source charges are fixed?
(b) Bound charges shift or turn and only partly oppose the applied field
Dielectric polarisation concerns bound charges. Complete equilibrium cancellation by mobile charges is the conductor mechanism.
Capacitor A has equal-area side-by-side dielectrics K=2 and K=6 across its gap. Capacitor B has the same plates and gap but the materials each occupy half the thickness over the full area. What is C_A:C_B?
(b) 4:3
Define for the same plate area and gap in vacuum.
In A, each material spans the full gap but has area . The regions share voltage and act in parallel: .
In B, each material has full area A and thickness . The layers act in series, with capacitances and : .
Thus and , neglecting edge effects as in the ideal parallel-plate model.
The plates of a capacitor carry +100 μC and -100 μC and are at potentials +25V and -25V. What is its capacitance?
(d) 2 μF
Use one plate-charge magnitude and the50V potential difference: C=Q/ΔV. The sum of plate charges is not the Q in this definition.
An air capacitor has capacitance 8pF. Its plate separation is halved and a dielectric of constant K=2 completely fills the gap. What is its new capacitance?
(a) 32 pF
C is proportional to K/d. Halving d gives factor2 and the dielectric gives factor K; for K=6 the textbook result is 96pF.
Three capacitors each 4μF form a network: two are in series in one branch, and the third is in parallel with that branch between the same terminals. What is the equivalent capacitance?
(c) 6 μF
The series pair gives 2μF. Add the parallel 4μF branch to obtain 6μF.
A 600pF capacitor is charged to 200V, isolated, then connected in parallel to an identical uncharged capacitor. How much electrostatic energy is lost after the transient?
(b) 6 μJ
Initial energy is CV²/2=12μJ. Charge sharing halves the voltage; total final energy is 6μJ, so 6μJ becomes heat and radiation.
Wrong
If electric potential is zero at a point, the electric field there must also be zero.
Why it feels right. Both quantities describe the same charges, so I expect them to cancel together.
Right
Potential adds as a scalar. Electric field adds as a vector.
Worked example
