The electric potential satisfies Laplace’s equation in a region when
A charges are present
B free charge density is zero
C conductivity is high
D dielectric constant changes
Laplace requires ρ = 0.
Line charge produces electric field that varies as
A 1/r²
B 1/r
C r
D constant
Infinite line charge → E=λ2πϵ0rE = \frac{\lambda}{2\pi \epsilon_0 r}E=2πϵ0rλ.
Potential inside a conductor is
A zero
B constant
C increasing radially
D infinite
Conductor is equipotential.
At the boundary of two dielectrics, the tangential component of E-field is
A constant
B zero
C continuous
D discontinuous
Et1=Et2E_{t1} = E_{t2}Et1=Et2.
Which quantity determines orientation of dipoles in dielectric?
A current
B external electric field
C magnetic field
D conductivity
E aligns dipoles.
Poisson’s equation expresses
A charge continuity
B relation between potential and charge
C Ohm’s law
D Faraday’s law
∇2V=−ρ/ϵ0\nabla^2 V = -\rho/\epsilon_0∇2V=−ρ/ϵ0.
Electric field near the surface of conductor is
A tangent to surface
B normal to surface
C random
D zero
E-field lines are perpendicular to conductor surface.
A capacitor’s energy for constant voltage decreases when dielectric inserted because
A C increases
B C decreases
C E increases
D charge decreases
U=12CV2U = \frac{1}{2}CV^2U=21CV2, so energy increases—BUT under constant V supply, the source removes energy → stored energy decreases.
Bound charge depends on
A E-field only
B P only
C J only
D conductivity
Bound charge ρb=−∇⋅P\rho_b = -\nabla \cdot Pρb=−∇⋅P.
In anisotropic dielectrics, permittivity is
A scalar
B vector
C tensor
D zero
Described using 3×3 permittivity tensor.
Drift velocity is typically
A high
B extremely low
C equal to thermal velocity
D equal to speed of light
~mm/s, very small.
Conductivity of intrinsic semiconductor increases with temperature because
A mobility increases
B carrier concentration increases
C permittivity increases
D resistivity increases
Electric flux density is given by
A E/ε
B εE
C 1/εE
D E²
D=εED = εED=εE.
Capacitance depends on
A geometry
B permittivity
C distance
D all of these
Dielectric with lower permittivity produces
A higher E inside
B lower E inside
C zero E
D infinite E
E=E0ϵrE = \frac{E_0}{\epsilon_r}E=ϵrE0.
In electrostatics, potential is unique if
A boundary potential given
B charges unknown
C field unknown
D conductivity unknown
Uniqueness theorem.
Energy stored between capacitor plates is proportional to
A E
B E²
C 1/E
D E³
u=12ϵE2u = \frac{1}{2}\epsilon E^2u=21ϵE2.
For parallel combination of capacitors
A same charge
B same voltage
C same current
D same energy
Electric displacement vector is used mainly
A to include free charge only
B to simplify Gauss law in dielectrics
C to calculate B field
D for conductors only
Conductivity increases with
A decreasing mobility
B decreasing electron density
C increasing carrier density
D increasing resistivity
In dielectric, induced dipole moment is proportional to
A temperature
B pressure
C electric field
D conductivity
Laplace equation cannot describe
A region without free charge
B region with uniform charge density
C potential between capacitor plates
D potential in air
Electric potential variance between two points relates to
A path taken
B E-field integral
C current
D magnetic flux
V=−∫E⋅dlV = -\int \mathbf{E}\cdot d\mathbf{l}V=−∫E⋅dl.
Capacitance decreases when
A area increases
B distance increases
C dielectric increases
D permittivity increases
Bound surface charge exists where
A P ⟂ surface
B P ∥ surface
C P = 0
D conductivity high
σb=P⋅n^\sigma_b = P \cdot \hat{n}σb=P⋅n^.
Clausius–Mossotti equation predicts
A molecular polarizability
B conductivity
C mobility
D resistivity
Electric current density direction is
A opposite E
B along E
C perpendicular to E
D random
For constant charge, inserting dielectric causes
A voltage increases
B voltage decreases
C energy increases
D capacitance decreases
Drift velocity is proportional to
A mobility
B electric field
C both A and B
D resistivity
Conductivity is
A q/μ
B n q μ
C E/J
D μ/J
A dielectric with stronger polarization produces
A larger D
B smaller D
C zero D
D opposite D
Poisson equation is used in
A capacitor without dielectric
B charged sphere problem
C potential in free space
D uniform field
Condition for surface E-field at conductor boundary
A Et = 0
B En = σ/ε₀
C Dn = 0
D P = 0
The Laplacian operator applied to constant potential gives
A constant
B zero
C infinite
D 1
A dielectric with zero susceptibility behaves like
A conductor
B vacuum
C perfect insulator
D plasma
Gauss law integral form applies to
A only dielectrics
B only conductors
C any closed surface
D only spheres
Potential due to infinite sheet of charge
A constant E
B constant V
C V varies linearly
D V = 0
E constant → V ∝ x.
Capacitance of cylindrical capacitor increases when
A inner radius increases
B outer radius increases
C length decreases
D permittivity increases
Heating effect in resistor due to
A electric field
B drift current
C collisions
D capacitance
Divergence of E in vacuum
A zero
B finite
C infinite
D negative
No free charge → ∇·E = 0.
Electric dipole field decreases as
A 1/r
B 1/r²
C 1/r³
D constant
Capacitance of isolated sphere
A proportional to radius
B inversely proportional
C independent of radius
D decreases with permittivity
C=4πϵ0RC = 4\pi \epsilon_0 RC=4πϵ0R.
Dielectric constant >1 means
A E inside > E outside
B E inside < E outside
C E = 0
D no polarization
Ohm’s law fails for
A conductors
B electrolytes
C superconductors
D nonlinear materials
Resistivity increases with
A increasing temperature in metals
B decreasing temperature in metals
C adding impurities
D both A and C
Boundary condition for D across dielectrics’ normal direction
A D1 = D2
B Dn changes by free charge
C Dn always zero
D Dn constant
Polarization current occurs due to
A electron drift
B dipole movement
C conduction
D resistive heating
Dielectric breakdown occurs when
A P = 0
B E exceeds critical value
C resistivity increases
D J = 0
Conductors shield electric field because
A charges distribute on surface
B dielectric effect
C magnetization
D electron absence
Permittivity tensor reduces to scalar when
A material isotropic
B field zero
C charges absent
D mobility high