Physics Quiz: Electrostatic Potential & Capacitance
1. A point charge q is rotated along a circle of radius r around another point charge Q. The work done by the electric field is:
2. The electric potential at a point due to an electric dipole is zero at:
3. Three capacitors of 3μF each are in series, then in parallel with another 3μF capacitor. Equivalent capacitance is:
4. If distance between plates is doubled and area is halved, capacitance becomes:
5. Which statement is true for an equipotential surface?
6. A dielectric slab is inserted into an isolated charged capacitor. What remains constant?
7. The SI unit of energy density of a capacitor is:
8. Two spheres of radii R₁ and R₂ (R₁ > R₂) have same potential. Ratio of charge densities σ₁/σ₂:
9. Potential at distance r from charge Q is V. Potential at 2r from charge 4Q is:
10. Dielectric introduced into a capacitor connected to a battery. Electric field:
11. Work done in moving 5μC from 10V to 40V is:
12. Capacitance of a spherical conductor of radius R is proportional to:
13. Energy stored in a 10μF capacitor charged to 50V:
14. In a region of constant potential, the electric field is:
15. Two capacitors C₁ > C₂ in series. Voltages V₁ and V₂ relate as:
Answer Key & Explanations
1. C Work done W = qΔV. On a circle around a central charge, the potential is the same at all points, so ΔV = 0.
2. B The potential of a dipole is V = (p cosθ) / (4πε₀r²). On the equatorial line, θ = 90°, so cosθ = 0.
3. B Series part: 1/Cs = 1/3 + 1/3 + 1/3 = 1 → Cs = 1μF. Parallel: Cp = 1 + 3 = 4μF.
4. C C = ε₀A/d. New C' = ε₀(A/2) / (2d) = (1/4)ε₀A/d.
5. B By definition, an equipotential surface has the same potential everywhere, so no work is needed to move a charge across it.
6. D For an isolated capacitor, there is no path for the charge to leave, so Q remains constant.
7. B Energy density is energy per unit volume, which is Joules per cubic meter (J/m³).
8. B V = σR/ε₀. For same V, σ ∝ 1/R. Thus σ₁/σ₂ = R₂/R₁.
9. C V ∝ Q/r. New V' ∝ (4Q)/(2r) = 2(Q/r). Hence V' = 2V.
10. C Since it's connected to a battery, V is constant. E = V/d. Since V and d are constant, E is constant.
11. A W = q(V₂ - V₁) = 5μC × (40V - 10V) = 150μJ.
12. A Capacitance of a sphere is C = 4πε₀R, so C ∝ R.
13. A U = ½CV² = ½ × 10⁻⁵ × 50² = ½ × 10⁻⁵ × 2500 = 1.25 × 10⁻² J.
14. B E = -dV/dr. If V is constant, its derivative is zero, so E = 0.
15. B In series, Q is same. V = Q/C. If C₁ > C₂, then V₁ < V₂.
