Each question has one correct answer, highlighted in green.
1) SI unit of electrostatic potential is:
2) Potential at a distance r from an isolated point charge Q (in vacuum) is:
- V = (1/4πϵ₀) · Q/r
- V = (1/4πϵ₀) · Q/r²
- V = (1/4πϵ₀) · r/Q
- V = (1/4πϵ₀) · Qr
3) Relation between electric field and potential is:
- E = ∇V
- E = -∇V
- V = ∇E
- V = -∇E
4) The potential due to multiple point charges equals:
- Product of individual potentials
- Vector sum of potentials
- Algebraic sum of scalar potentials
- Zero if charges are equal and opposite
5) Work done by the electric field in moving a charge between two points equals:
- q(V_final + V_initial)
- q(V_initial − V_final)
- q(V_final − V_initial) always positive
- Independent of potential difference
6) In electrostatic equilibrium, the electric field inside a conductor is:
- Uniform and non-zero
- Zero at the center only
- Zero everywhere inside
- Parallel to the surface
7) The surface of a conductor in electrostatic equilibrium is:
- At varying potential
- Potential depends on position
- An equipotential surface
- Potential equals zero only
8) The capacitance C is defined by:
- C = V/Q
- CV = Q²
- C = Q/V
- C = V²/Q
9) SI unit of capacitance is:
10) For a parallel-plate capacitor (vacuum) with plate area A and separation d:
- C = ϵ₀ d / A
- C = ϵ₀ A / d
- C = A / (ϵ₀ d)
- C = d / (ϵ₀ A)
11) With dielectric of relative permittivity κ inserted fully between plates, capacitance becomes:
12) Energy stored in a capacitor carrying charge Q and potential V is:
- U = QV
- U = ½ QV
- U = Q²V
- U = ½ V/Q
13) Equivalent capacitance for capacitors in series satisfies:
- 1/C_eq = Σ (1/Cᵢ)
- C_eq = Σ Cᵢ
- C_eq = Π Cᵢ
- C_eq = max(Cᵢ)
14) In parallel combination of capacitors:
- Same charge on each
- Same potential across each
- Same energy in each
- Same charge density
15) In series combination of capacitors:
- Same potential across each
- Same charge on each
- Same capacitance for each
- Same energy for each
16) The energy density of an electric field in vacuum is:
- u = ϵ₀/E²
- u = ½ ϵ₀ E²
- u = ½ E/ϵ₀
- u = ϵ₀² E
17) For a uniform electric field E, the potential difference between points separated by distance d along field is:
- ΔV = -E d
- ΔV = +E d
- ΔV = -E/d
- ΔV = 0
18) Equipotential surfaces are always:
- Parallel to electric field lines
- Perpendicular to electric field lines
- Coincident with field lines
- Randomly oriented
19) Potential at the center of a uniformly charged ring (total charge Q, radius R) is:
- 0
- V = (1/4πϵ₀) · Q/R
- V = (1/4πϵ₀) · Q/R²
- V = (1/4πϵ₀) · R/Q
20) Potential at the center of a uniformly charged solid sphere (total charge Q, radius R) is:
- V = (1/4πϵ₀) · (3Q/2R)
- V = (1/4πϵ₀) · (Q/2R)
- V = 0
- V = (1/4πϵ₀) · (2Q/R)
21) A conductor cavity enclosing no charge has electric field inside the cavity equal to:
- Non-zero uniform
- Zero
- Depends on external field
- Infinite
22) When a dielectric slab completely fills a capacitor while disconnected from battery, charge on plates:
- Increases
- Remains same
- Decreases
- Becomes zero
23) In the same situation (dielectric inserted, battery disconnected), potential difference:
- Increases
- Decreases by factor κ
- Unchanged
- Becomes zero
24) If the battery remains connected while inserting dielectric, the charge on plates:
- Increases by factor κ
- Decreases
- Unchanged
- Becomes zero
25) Dimensions of ϵ₀ (permittivity of free space) are:
- [M⁻¹ L⁻³ T⁴ A²]
- [M L T⁻²]
- [M L² T⁻²]
- [M⁰ L⁰ T⁰]
26) Potential difference between plates of a charged parallel-plate capacitor with uniform field E and separation d is:
- V = Ed²
- V = E d
- V = E/d
- V = E² d
27) For two capacitors C and 2C in series across V, potential across C is:
28) For two capacitors C and 2C in parallel across V, charge on 2C is:
- Q = 2C · V
- Q = C · V
- Q = V/2C
- Q = V/C
29) Electric field just outside a charged conductor surface (surface charge density σ) is:
- E = σ/ϵ₀ (tangent)
- E = σ/ϵ₀ (normal outward)
- E = 0
- E = 2σ/ϵ₀ (tangent)
30) Potential difference between two points on the same equipotential surface is:
- Positive
- Negative
- Zero
- Depends on path
31) If V = ax² (a > 0), the electric field along x is:
- E = -2ax (along −x for x>0)
- E = +2ax
- E = ax
- E = -ax²
32) A capacitor is charged to V and disconnected; if plate separation is doubled (vacuum), final potential becomes:
33) For a spherical capacitor with inner radius a and outer radius b (vacuum), capacitance is:
- C = 4πϵ₀ ab
- C = 4πϵ₀ ab/(b − a)
- C = 4πϵ₀ (b − a)/ab
- C = 4πϵ₀ (a + b)
34) For a cylindrical capacitor (coaxial) per unit length with radii a < b, capacitance per length is:
- C′ = 2πϵ₀ / ln(b/a)
- C′ = 2πϵ₀ ln(b/a)
- C′ = ϵ₀ ln(a/b)
- C′ = 2π/ϵ₀ ln(b/a)
35) A dielectric reduces the internal electric field primarily because of:
- Increase in free charges
- Polarization and bound surface charges
- Temperature rise
- Magnetic effects
36) Potential due to an electric dipole (p) at a point on axial line at distance r (r ≫ size):
- V = (1/4πϵ₀) · p/r²
- V = (1/4πϵ₀) · p/r³
- V = (1/4πϵ₀) · pr
- V = (1/4πϵ₀) · p/r
37) Potential due to a dipole at a point on the equatorial line (r ≫ size):
- V = (1/4πϵ₀) · p/r²
- V = 0
- V = (1/4πϵ₀) · 2p/r²
- V = (1/4πϵ₀) · p/r
38) For V = kQ/r, as r → ∞, the potential tends to:
39) If a metal sphere is given some charge, it resides:
- Uniformly throughout the volume
- Only on the outer surface
- Only at the center
- On inner and outer surfaces equally
40) Capacitance depends on:
- Geometry and dielectric medium
- Potential alone
- Charge alone
- Mass of plates
41) The potential at the surface of a charged conductor is highest at:
- Flatter regions
- Sharper (smaller radius) regions for field; potential is uniform over the conductor
- All points different
- Depends on environment only
42) Capacitors in series have equivalent capacitance:
- Less than the smallest individual C
- Between smallest and largest C
- Greater than largest C
- Equal to sum of all C
43) Capacitors in parallel have equivalent capacitance:
- Less than the smallest C
- Between smallest and largest C
- Equal to sum of all C
- Equal to harmonic mean
44) If Q is kept constant and C is doubled, the stored energy:
- Quadruples
- Doubles
- Halves
- Unchanged
45) If V is kept constant and C is doubled, the stored energy:
- Halves
- Doubles
- Unchanged
- Reduces to one-fourth
46) The capacitance of an isolated conducting sphere of radius R (vacuum) is:
- C = 4πϵ₀ R
- C = 4πϵ₀ / R
- C = ϵ₀ / (4πR)
- C = R / (4πϵ₀)
47) Which is true for an ideal capacitor?
- Stores charge with energy loss
- Blocks DC (after charging) and allows AC (reactively)
- Converts electric energy to heat
- Provides a constant current source
48) The SI unit of 1/(4πϵ₀) is closest to:
49) For a given capacitor, breakdown occurs when:
- Q exceeds a certain value regardless of V
- Electric field exceeds the dielectric strength
- Temperature is absolute zero
- Plates are too wide
50) Which change increases capacitance of a parallel-plate capacitor the most?
- Increase plate separation
- Decrease plate area
- Insert higher-κ dielectric fully
- Reduce ϵ₀