Chapter 7: Electrostatics, Dielectrics & Current Electricity (Set-2)

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

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

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

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