The magnetic field at a distance r from a long straight current-carrying wire varies as
A 1/r²
B r
C 1/r
D Constant
Biot–Savart law gives B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}B=2πrμ0I, so B∝1/rB \propto 1/rB∝1/r.
The direction of magnetic field produced by a current-carrying conductor is given by
A Fleming’s left-hand rule
B Maxwell’s right-hand corkscrew rule
C Right-hand palm rule
D Lenz’s law
Maxwell’s corkscrew (or right-hand thumb rule) determines circular field direction.
The magnetic field at the center of a circular loop of radius R carrying current I is
A μ0I4R
B μ0I2R
C μ0I8R
D μ0IR
Standard result: B=μ0I2RB = \frac{\mu_0 I}{2R}B=2Rμ0I.
The SI unit of magnetic field intensity (H) is
A Tesla
B Weber
C A/m
D Henry
H-field units = A/m.
Ampere’s circuital law is valid for
A Electrostatics only
B Time-varying fields only
C Steady currents
D Alternating currents only
Original Ampere’s law applies strictly to steady currents.
Ampere’s law in integral form is
A ∮E⋅dl=0
B ∮B⋅dl=μ0Ienc
C ∇⋅B=0
D ∇×E=−∂B/∂t
This is the basic form of Ampere’s circuital law.
Hall voltage is directly proportional to
A Current only
B Magnetic field only
C Both current and magnetic field
D Resistivity of conductor
VH=IBnqtV_H = \frac{IB}{nqt}VH=nqtIB → proportional to I and B.
Hall coefficient is inversely proportional to
A Charge density of carriers
B Magnetic field
C Drift velocity
D Resistivity
RH=1nqR_H = \frac{1}{nq}RH=nq1.
A material with negative Hall coefficient must have
A Holes as majority carriers
B Electrons as majority carriers
C No charge carriers
D Magnetic ordering
Negative sign → electrons dominate.
Diamagnetic materials are characterized by
A Permanent dipole moments
B Strong attraction to magnetic field
C Relative permeability < 1
D Hysteresis loops with large area
Diamagnetism: weak repulsion, μr < 1.
Paramagnetic materials have
A No atomic dipoles
B Permanent dipoles that align weakly with B
C Strong magnetic ordering
D μr < 1
Ferromagnetism occurs due to
A Induced dipoles
B Random thermal motion
C Exchange interactions between neighboring atoms
D Zero magnetic domain structure
The area of a ferromagnetic hysteresis loop represents
A Resistivity
B Magnetic flux
C Magnetic energy loss per cycle
D Magnetic intensity
Which of the following is temperature-dependent (strongly)?
A Diamagnetism
B Paramagnetism
C Both A and B
D None
Paramagnetism follows Curie’s law: χ ∝ 1/T.
EM induction was discovered by
A Maxwell
B Faraday
C Ampere
D Tesla
Faraday’s law states that induced emf is
A Proportional to flux
B Proportional to rate of change of flux
C Constant for constant flux
D Zero for moving conductor
Lenz’s law ensures
A Charge conservation
B Energy conservation
C Flux remains constant
D Magnetic monopoles exist
A coil rotating in a uniform B-field produces
A DC supply
B Pulsating DC
C Pure sine-wave AC
D Square-wave AC
Self-inductance depends on
A Number of turns
B Area
C Permeability
D All of these
Mutual inductance is maximum when
A Flux linkage is minimum
B Coils are perpendicular
C Coils share maximum common flux
D Coils are far apart
The unit of inductance is
A Weber
B Henry
C Tesla
D Volt
In an LR circuit, current rises to 63% of maximum in time equal to
A RL
B L/R
C 1/RC
D L²/R
The induced electric field in EMI is
A Conservative
B Non-conservative
C Zero
D Only magnetic
Curl E ≠ 0 in time-varying B.
AC generator output depends on
A Angular speed
B Magnetic field
C Coil area
D All of these
An inductor in AC behaves as
A Resistive element
B Capacitive element
C Voltage leads current
D Current leads voltage
The reactance of an inductor is
A XL=1ωC
B XL=ωL
C XL=1L
D XL=RC
The power factor of a purely inductive circuit is
A 0
B 1
C 0.5
D -1
φ = 90°, cosφ = 0.
The EMF equation of an AC generator includes
A Number of turns
B Angular velocity
C Magnetic flux
D All of these
Skin effect increases with
A Decreasing frequency
B Increasing frequency
C Zero frequency
D High resistance
Skin depth varies as
A δ∝ω
B δ∝1/ω
C δ independent of ω
D δ → ∞
δ=2μσω\delta = \sqrt{\frac{2}{\mu\sigma\omega}}δ=μσω2.
In good conductors, EM waves
A Propagate without attenuation
B Are heavily attenuated
C Gain energy
D Remain unchanged
Maxwell added displacement current term to
A Ohm’s law
B Ampere’s law
C Gauss law
D Faraday law
Displacement current exists
A Only in vacuum
B Only in metals
C Only in dielectrics
D In any region with changing electric field
Maxwell’s correction made Ampere’s law consistent with
A Charge conservation
B Coulomb’s law
C Newton’s laws
D Thermodynamics
The speed of EM waves in vacuum is given by
A 1/√(μϵ)
B √(μϵ)
C μϵ
D None
The Poynting vector represents
A Force
B Energy flow density
C Electric potential
D Magnetic flux
Unit of Poynting vector is
A W/m²
B J/m²
C N/C
D C/m²
The direction of Poynting vector is
A E direction
B B direction
C E × B
D B × E
Poynting theorem deals with
A Energy conservation in EM fields
B Charge conservation
C Momentum of particles
D Light refraction
EM waves are
A Longitudinal
B Transverse
C Both
D None
In EM waves, E and B are
A Perpendicular
B Parallel
C Random
D Opposite
EM wave carries
A Only electric energy
B Only magnetic energy
C Both electric and magnetic energy
D No energy
Magnetic energy density is
A 1/2 ϵE²
B 1/2 μH²
C EH
D EB
Wave impedance of free space is
A 50 Ω
B 75 Ω
C 200 Ω
D 377 Ω
In good conductors, phase difference between E and B is approximately
A 0°
B 45°
C 90°
D 180°
Anomalous dispersion occurs when
A Frequency increases slowly
B dn/dω < 0
C dn/dω > 0
D Refractive index constant
Ferromagnetism disappears above
A Curie temperature
B Transition temperature
C Melting point
D Debye temperature
Magnetic susceptibility of diamagnetic materials is
A Positive large
B Negative small
C Positive small
D Zero
The displacement current density is
A ϵE
B ϵ∂E/∂t
C μH
D σE
EM waves satisfy
A Poisson equation
B Laplace equation
C Wave equation
D Bernoulli equation