The electrostatic field is defined as
A E⃗=−∇V
B E⃗=∇V
C E⃗=∇2V
D E⃗=−∂V/∂t
In electrostatics, the field is conservative and equals the negative gradient of potential.
For a point charge, the electric field varies as
A 1/r
B 1/r²
C r
D Constant
Coulomb’s law gives E∝1/r².
Which equation is valid in a charge-free region?
A Poisson’s equation
B Laplace’s equation
C Gauss’s law
D Ampere’s law
Laplace’s equation: ∇²V = 0 when ρ = 0.
Poisson’s equation is expressed as
A ∇²V = 0
B ∇²V = ρ
C ∇²V = −ρ/ϵ₀
D ∇²V = ϵ₀ρ
Standard form: ∇²V = −ρ/ϵ₀.
Potential difference between two points is defined as
A Work done per charge
B Work done per mass
C Force per unit charge
D Charge per unit work
V = W/q.
The capacitance of a parallel-plate capacitor with dielectric is
A decreases by κ
B increases by κ
C increases by 1/κ
D independent of dielectric
C = κϵ₀A/d.
Polarization P⃗ is defined as
A charge conductivity
B dipole moment per unit volume
C dielectric strength
D electric flux density
P⃗ = dipole moment/volume.
The D-vector is related to E by
A D⃗ = ϵ₀E⃗
B D⃗ = ϵE⃗
C D⃗ = P⃗ + ϵ₀E⃗
D All of these
All relations are valid in different contexts; (C) is general.
In a conductor, electric field inside is
A very large
B zero
C infinite
D variable
Charges rearrange to cancel internal field.
Microscopic form of Ohm’s law is
A J⃗ = σE⃗
B J⃗ = ρE⃗
C E⃗ = σJ⃗
D J⃗ = σV
Current density proportional to electric field.
Conductivity is defined as
A reciprocal of resistivity
B resistance per length
C charge density
D permittivity
Electric potential due to a dipole varies as
A 1/r
B 1/r²
C 1/r³
D constant
Dipole potential V∝1/r².
Laplace equation holds for
A linear dielectrics only
B any region without free charge
C conductors only
D non-polar materials
Capacitance of spherical capacitor depends on
A radius only
B permittivity only
C geometry and permittivity
D potential applied
Bound charge density is
A ρb = −∇⋅P⃗
B ρb = ∇⋅P⃗
C ρb = σE⃗
D ρb = ρf
Surface bound charge density is
A σb = P⃗⋅n̂
B σb = P⃗×n̂
C σb = P⃗⋅E⃗
D zero always
Clausius–Mossotti equation relates
A polarization to resistivity
B permittivity to polarizability
C conductivity to mobility
D flux to charge
Clausius–Mossotti equation is written as
A (ϵ−1)/(ϵ+2)=Nα/(3ϵ₀)
B ϵ = αN
C ϵ = 3α
D ϵ = 1 + 2α
Current density is
A current per unit area
B charge per unit volume
C field per charge
D conductivity per unit mass
Drift velocity is proportional to
A electric field
B charge density
C resistivity
D mobility only
Mobility μ is defined as
A J/σ
B vd/E
C σE
D E/vd
For a dielectric, polarization is proportional to
A electron mass
B applied electric field
C resistivity
D none
Electric displacement D accounts for
A bound charge only
B free charge only
C total charge
D only conduction charges
Gauss’s law in differential form
A ∇⋅E⃗ = ρ
B ∇⋅E⃗ = ρ/ϵ₀
C ∇²E = 0
D ∇×E = 0
Laplace equation implies potential is
A linear
B harmonic
C exponential
D discontinuous
Capacitance increases when
A plate area decreases
B separation increases
C dielectric constant increases
D vacuum replaced by conductor
In dielectrics at equilibrium
A free charges move
B polarization remains constant
C bound charges become zero
D conductivity becomes infinite
Electric flux is measured in
A Volt
B Coulomb
C Newton-meter
D C·m²
A conductor with zero resistivity behaves as
A insulator
B perfect conductor
C dielectric
D semiconductor
Resistivity varies with
A temperature
B field
C potential
D geometry
For anisotropic dielectrics
A P⃗ ∥ E⃗ always
B Polarization depends on direction
C dielectric constant = 1
D no polarization
Electric field inside a cavity of conductor (no charges)
A zero
B infinite
C finite
D depends on voltage
Potential is lower where field is
A zero
B uniform
C pointing toward that point
D pointing away
Relative permittivity is
A always > 1
B can be < 1
C always < 1
D always infinite
For plasmas/metals, effective εr < 1.
Energy stored in capacitor is
A 1/2 CV²
B CV
C IV
D 1/2 V/C
Dielectric breakdown occurs when
A conductivity becomes zero
B E exceeds critical value
C P becomes infinite
D C becomes zero
Polarization charge exists
A only in metals
B only in dielectrics
C in all materials
D in vacuum
D-field boundary condition normal component
A continuous always
B discontinuous by surface free charge
C discontinuous by bound charge
D independent of charge
Microscopic current relation
A J⃗ = nqμE⃗
B J⃗ = E/μ
C J⃗ = nE
D J⃗ = qE
Conductivity depends on
A carrier concentration
B mobility
C charge
D all of these
Electric potential inside conductor is
A zero
B constant
C increasing
D decreasing
Poisson equation is used when
A no charges present
B free charge density exists
C dielectric is nonlinear
D field is zero
Capacitance of series capacitors
A sum of all
B reciprocal of sum of reciprocals
C product/sum
D twice the individual
In polarization, induced dipoles align
A randomly
B opposite to E
C with E
D perpendicular
In an ideal dielectric
A no energy stored
B no conduction
C no polarization
D infinite conductivity
The D-field in vacuum equals
A ε₀E
B PE
C E/P
D 0
Relaxation time of conductor relates to
A voltage
B conductivity
C resistivity
D dielectric constant
Clausius–Mossotti equation is valid for
A solids only
B dilute isotropic dielectrics
C conductors
D superconductors
Resistivity of semiconductor
A decreases with temperature
B increases with temperature
C independent of temperature
D becomes infinite
Electric susceptibility relates
A P to D
B P to E
C D to V
D J to E