Gauss’s law relates closed-surface electric flux to what quantity?
A Ampère’s law
B Faraday’s law
C Gauss’s law
D Biot–Savart law
Answer: C. Gauss’s law. Gauss’s law states that the outward flux of D equals enclosed free charge.
Electric field strength is measured in which SI unit?
A V/m
B A/m
C Wb/m²
D C/N
Answer: A. V/m. Electric field is force per unit charge, measured in volts per metre.
How is electrostatic potential related to electric field?
A Current-density divergence
B Positive potential gradient
C Magnetic-field curl
D Negative potential gradient
Answer: D. Negative potential gradient. The electrostatic field is E = −∇V.
Under electrostatic conditions, what is ∇×E?
A ρ/ε
B Zero
C ∂B/∂t
D μJ
Answer: B. Zero. Faraday’s law gives zero curl when the magnetic field is static.
Inside a perfect conductor at equilibrium, the electric field is?
A Radial
B Zero
C Infinite
D Uniform
Answer: B. Zero. Free charges redistribute until the internal electrostatic field vanishes.
By what distance law does a point-charge field decrease?
A Constant
B Inverse cube
C Direct square
D Inverse square
Answer: D. Inverse square. Coulomb’s field magnitude varies as 1/r².
From which law is the field of a current element found?
A Biot–Savart law
B Gauss’s law
C Faraday’s law
D Lenz’s law
Answer: A. Biot–Savart law. The Biot–Savart law gives the magnetic-field contribution of a current element.
Magnetic flux uses which SI unit?
A Henry
B Ampere
C Weber
D Tesla
Answer: C. Weber. Magnetic flux is measured in webers.
Absence of magnetic monopoles is expressed by which equation?
A ∇·B = 0
B ∇×H = J
C ∇×E = 0
D ∇·D = ρ
Answer: A. ∇·B = 0. Gauss’s law for magnetism says B has zero divergence.
According to Lenz’s law, induced current opposes what?
A Resistance change
B Charge density
C Flux change
D Field direction
Answer: C. Flux change. The induced effect opposes the change in magnetic flux that produces it.
Ampère’s law gains which current term?
A Eddy current
B Displacement current
C Leakage current
D Convection current
Answer: B. Displacement current. Maxwell added displacement current to make Ampère’s law consistent with time-varying fields.
In vacuum, what expression determines electromagnetic wave speed?
A 1/(μ₀ε₀)
B μ₀ε₀
C √(μ₀ε₀)
D 1/√(μ₀ε₀)
Answer: D. 1/√(μ₀ε₀). The vacuum wave speed is c = 1/√(μ₀ε₀).
When E×H is evaluated for a plane wave, which way does it point?
A Electric-field direction
B Magnetic-field direction
C Propagation direction
D Surface normal
Answer: C. Propagation direction. The Poynting vector E×H points along the direction of energy propagation.
Electromagnetic power flow per area is represented by which vector?
A Poynting vector
B Magnetic potential
C Current density
D Electric flux density
Answer: A. Poynting vector. The Poynting vector gives electromagnetic power-flow density.
On an electrostatic equipotential surface, the electric field points how?
A Along the surface
B Tangentially
C Randomly
D Perpendicularly
Answer: D. Perpendicularly. The potential has no tangential change along an equipotential surface.
Within a source-free electrostatic region, which equation does V satisfy?
A Wave equation
B Laplace equation
C Diffusion equation
D Helmholtz equation
Answer: B. Laplace equation. With zero charge density, Poisson’s equation reduces to Laplace’s equation.
Why does steady current create magnetic-field circulation around a loop?
A Enclosed current
B Magnetic charge
C Electric flux
D Enclosed voltage
Answer: A. Enclosed current. Ampère’s circuital law relates circulation of H to enclosed current.
Local charge conservation is expressed by which equation?
A Constitutive equation
B Wave equation
C Laplace equation
D Continuity equation
Answer: D. Continuity equation. The continuity equation balances current divergence with charge accumulation.
Where is capacitance measured in SI?
A Weber
B Farad
C Tesla
D Coulomb
Answer: B. Farad. One farad equals one coulomb per volt.
How does a dielectric increase ideal capacitance?
A Lower plate area
B Lower charge
C Higher permittivity
D Higher resistance
Answer: C. Higher permittivity. A dielectric raises permittivity and therefore capacitance for fixed geometry.
Energy density in a linear dielectric is given by what expression?
A μH²
B E×H
C ρv
D ½ E·D
Answer: D. ½ E·D. The electrostatic energy density is one half E dot D.
For a uniform plane wave, the longitudinal E and H components are?
A Zero
B Equal
C Infinite
D Time varying
Answer: A. Zero. A uniform plane wave is transverse to its propagation direction.
Stokes’ theorem converts a curl surface integral into what boundary integral?
A Green’s theorem
B Stokes’ theorem
C Divergence theorem
D Gauss’s theorem
Answer: B. Stokes’ theorem. Stokes’ theorem relates surface curl to circulation around its boundary.
For a uniform plane wave, what does intrinsic impedance equal?
A Charge-to-current ratio
B Magnetic-to-electric flux
C Electric-to-magnetic field ratio
D Power-to-area ratio
Answer: C. Electric-to-magnetic field ratio. Intrinsic impedance is the magnitude ratio |E|/|H|.
Integrating conduction-current density over an area yields which quantity?
A Conduction current
B Electric flux
C Magnetic flux
D Stored charge
Answer: A. Conduction current. The surface integral of J gives current crossing that surface.