A region where ∇×E⃗ = 0 implies
A electric field is non-conservative
B electric field is conservative
C magnetic field is constant
D potential does not exist
Curl-free electric fields are conservative, allowing a scalar potential.
A conductor in electrostatic equilibrium has
A uniform electric field inside
B zero electric field inside
C infinite electric field inside
D non-zero but constant field
Which expression represents potential of a point charge?
A V = q / (4πϵ₀r)
B V = qr
C V = qr²
D V = q/r²
For a one-dimensional potential, Poisson’s equation reduces to
A dV/dx = 0
B d²V/dx² = −ρ/ϵ₀
C d²V/dx² = 0
D dV/dx = ρ
Laplace’s equation implies
A potential has local maxima
B potential has local minima
C potential has no local maxima or minima inside the region
D field must be zero
Harmonic functions satisfy the maximum–minimum principle.
For a capacitor with dielectric partially inserted, capacitance
A increases
B decreases
C remains unchanged
D becomes zero
Electric susceptibility χe is related to permittivity as
A ϵ = ϵ₀(1 + χe)
B ϵ = ϵ₀χe
C ϵ = χe
D χe = 1
Bound surface charge is produced due to
A free electrons
B polarization
C conduction current
D magnetic field
D-field obeys Gauss’s law
A for free charges
B for bound charges
C for total charges
D only for conductor
A dielectric with high polarizability has
A low permittivity
B high permittivity
C zero susceptibility
D high resistivity only
Clausius–Mossotti equation connects
A atomic polarizability with macroscopic permittivity
B conductivity with temperature
C boundary conditions
D Gauss and Ampere laws
Macroscopic Ohm’s law is
A J⃗ = σE⃗
B V = IR
C E = ρJ
D R = σL
The drift velocity is
A random velocity
B slow average velocity due to E-field
C thermal velocity
D independent of field
Conductivity of metals
A increases with temperature
B decreases with temperature
C unaffected by temperature
D becomes zero at high T
More lattice scattering at high temperature.
Permittivity of vacuum is
A 8.85 × 10⁻¹² F/m
B 1
C 9.8 × 10⁻¹⁰
D 0
Electric energy density is
A ½ϵE²
B ϵE
C ½σE²
D E²/2
A dielectric slab inserted in capacitor reduces
A stored energy for constant charge
B capacitance
C E-field to zero
D potential to zero
A perfect dielectric has
A zero conductivity
B infinite conductivity
C zero permittivity
D infinite permittivity
If uniform polarization exists, bound surface charge appears on
A internal surfaces only
B external surfaces only
C both internal and external
D nowhere
Laplace’s equation ensures
A potential uniquely determined by boundary conditions
B potential independent of boundary conditions
C infinite solutions
D zero potential
Divergence of D equals
A free charge density
B bound charge density
C total charge density
D zero
For a parallel-plate capacitor, electric field is
A zero
B uniform
C non-uniform
D parabolic
Ohmic materials satisfy
A linear relation between J and E
B exponential relation
C random relation
D no relation
Resistivity is measured in
A ohm-meter
B ohm
C siemens
D farad
In electrostatics, the curl of E is
A zero
B constant
C proportional to charge
D undefined
Dielectric constant is the ratio
A ϵ / ϵ₀
B ϵ₀ / ϵ
C ϵ / σ
D σ / ϵ₀
Electric dipole moment is
A q × r
B qr²
C q / r
D q / r²
In an isotropic dielectric
A P depends on direction
B P always parallel to E
C E always perpendicular to P
D no polarization
Drift current density is
A σE
B nqvd
C both A and B
D none
Electrical conductivity unit is
A S/m
B ohm
C V/m
D J/C
The potential of a conductor is
A uniform
B zero always
C depends on shape
D infinite
Poisson equation in spherical symmetry reduces to
A (1/r²)d/dr(r² dV/dr) = −ρ/ϵ₀
B d²V/dr² = −ρ
C ∇²V = 0
D none
E-field inside dielectric
A equals external field
B less than external field
C greater than external field
D zero
Capacitance in series decreases because
A effective separation increases
B area reduces
C permittivity increases
D resistance increases
Bound volume charge appears when
A polarization varies in space
B polarization constant
C conductor used
D dielectric removed
The polarization vector represents
A free charge distribution
B magnetization
C dipole density
D current density
Relaxation time of a conductor is
A ϵ / σ
B σ / ϵ
C ϵσ
D 1 / (ϵσ)
For cubic crystals, dielectric constant
A anisotropic
B isotropic
C zero
D infinite
Free charge distribution determines
A boundary conditions
B potential uniquely
C field uniquely
D all of these
Conductors have
A tightly bound electrons
B free electrons
C no electrons
D only ions
Energy stored per unit volume in dielectric is
A ½ E · D
B ED
C ½ σE
D σD
A good dielectric has
A low ε
B high ε
C high σ
D low breakdown strength
Laplace equation applicable to
A free charge region only
B region with no free charge
C conductor surface
D only dielectrics
The displacement current exists in
A conductors only
B dielectrics only
C vacuum and dielectrics
D nowhere
Conductivity σ is
A proportional to charge carrier mobility
B proportional to carrier density
C proportional to charge
D all of these
Potential difference in uniform field
A E · d
B Ed²
C 1 / Ed
D zero
Dielectric loss occurs due to
A conduction current
B polarization lag
C both A & B
D none
Clausius–Mossotti equation applies to
A dense solids
B dilute gases
C superconductors
D semiconductors
Metallic conductors obey Ohm’s law because
A scattering time constant
B drift velocity proportional to E
C electrons behave classically
D all of these
In dielectrics, E-field lines
A remain unchanged
B bend inside
C disappear
D reverse direction