Why does electrostatic work around a closed path vanish?
A Radiating field
B Conservative field
C Magnetic field
D Resistive field
Answer: B. Conservative field. An electrostatic field is conservative, so its closed-path line integral is zero.
In differential form, ∇·D equals what?
A Electric potential
B Current density
C Magnetic flux
D Free charge density
Answer: D. Free charge density. Gauss’s electric law gives ∇·D = ρfree.
What is the capacitance of ideal parallel plates?
A εA/d
B εd/A
C A/(εd)
D d/(εA)
Answer: A. εA/d. For uniform dielectric between plates, C = εA/d.
If ideal plate separation doubles, capacitance becomes what fraction?
A Four times
B Unchanged
C One half
D Twice
Answer: C. One half. Capacitance is inversely proportional to plate separation.
How is V(B)−V(A) obtained from E along a path?
A ∫Aᴮ B·dS
B +∫Aᴮ E·dl
C ∫Aᴮ H·dl
D −∫Aᴮ E·dl
Answer: D. −∫Aᴮ E·dl. Potential difference equals the negative line integral of E.
For a point charge, how does E scale with radius?
A Inverse first power
B Inverse square
C Direct square
D Constant
Answer: B. Inverse square. Coulomb’s law gives an inverse-square field.
Where does excess electrostatic charge reside on a conductor?
A At the centre
B In the lattice
C Surface
D Uniformly inside
Answer: C. Surface. At electrostatic equilibrium, excess charge resides on the conductor’s surface.
When equipotential lines crowd closer, the field becomes?
A Stronger
B Unchanged
C Weaker
D Zero
Answer: A. Stronger. A larger potential change over a shorter distance means a stronger field.
Which SI unit measures electric potential?
A Farad
B Volt
C Coulomb
D Ohm
Answer: B. Volt. Electric potential is measured in volts.
Around a long straight current, magnetic-field lines form?
A Parallel lines
B Closed spheres
C Concentric circles
D Radial lines
Answer: C. Concentric circles. The right-hand rule gives circular magnetic-field lines around a straight current.
Use which rule to find the direction of qv×B?
A Right-hand rule
B Gauss’s law
C Left-hand rule
D Lenz’s law
Answer: A. Right-hand rule. The cross product qv×B follows the right-hand rule for positive charge.
Why does magnetic force do no work on a moving point charge?
A Force parallel to velocity
B Charge stays constant
C Field is uniform
D Force perpendicular to velocity
Answer: D. Force perpendicular to velocity. The magnetic force is perpendicular to velocity, so it does no work.
What is the SI unit of magnetic-field strength H?
A Weber
B Henry
C A/m
D Tesla
Answer: C. A/m. H is measured in amperes per metre.
Within a linear magnetic material, how are B and H related?
A B = μH
B B = μ + H
C B = εH
D B = H/μ
Answer: A. B = μH. For a linear isotropic medium, B = μH.
How does changing magnetic flux produce an electric field?
A Static potential only
B Zero electric field
C Surface charge only
D Nonconservative circulation
Answer: D. Nonconservative circulation. Faraday induction gives a nonzero closed-loop circulation of E.
For a static electric field, what is its curl?
A μJ
B Zero
C ∂D/∂t
D ρ/ε
Answer: B. Zero. In electrostatics, Faraday’s law reduces to ∇×E = 0.
Across any closed surface, net magnetic flux is what?
A Always positive
B Enclosed current
C Zero
D Surface charge
Answer: C. Zero. With no magnetic monopoles, Gauss’s magnetic law gives zero net flux.
At a dielectric boundary, the jump in normal D equals what?
A Conduction current
B Tangential E
C Magnetic flux
D Free surface charge
Answer: D. Free surface charge. The normal-D discontinuity equals free surface-charge density.
At a perfect-conductor boundary, tangential E is?
A Zero
B Continuous but nonzero
C Normal to surface
D Maximum
Answer: A. Zero. The electric field tangent to an ideal conductor surface vanishes.
How is relative permittivity defined?
A εμ
B ε/ε₀
C ε₀/ε
D μ/ε
Answer: B. ε/ε₀. Relative permittivity is the ratio of material to vacuum permittivity.
Express wavelength using phase velocity and frequency.
A vf
B f/v
C 2πvf
D v/f
Answer: D. v/f. Wavelength equals phase velocity divided by frequency.
What does attenuation constant quantify?
A Amplitude decay per length
B Power per area
C Frequency change per metre
D Phase change per cycle
Answer: A. Amplitude decay per length. The attenuation constant describes exponential field-amplitude decay with distance.
Under an ideal lossless-material model, conductivity is?
A Frequency dependent
B Zero
C Infinite
D Negative
Answer: B. Zero. An ideal lossless dielectric has zero conductivity.
Which coordinates suit an isolated point-charge field?
A Cartesian coordinates
B Cylindrical coordinates
C Spherical coordinates
D Elliptic coordinates
Answer: C. Spherical coordinates. Spherical symmetry makes the point-charge field simplest in spherical coordinates.
In a vacuum plane wave, electric and magnetic energy densities are?
A Equal
B Both zero
C Always unequal
D Unrelated
Answer: A. Equal. For a plane wave in vacuum, the electric and magnetic energy densities are equal.