Electromagnetic Fields MCQ – 28 previous year questions with solutions

Capacitance is C = Q/V, so V = Q/C. With Q=28 C and C=12 mF, V=28/0.012≈2333 V=2.33 kV.

In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. The conductor is then an equipotential body and excess free charge resides on its surface. Key relation: Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant.

Exam focus: Zero internal E and constant potential are two views of the same equilibrium condition. Common trap: The field does not increase with depth inside an ideal conductor.

A conservative electrostatic field has zero closed-loop line integral, path-independent potential difference and zero curl in a simply connected electrostatic region. Conservativeness does not mean the electric field has zero divergence everywhere, because divergence is related to charge density. The statement in option C is therefore the one we do not mean.

At r = 3 m only the cylindrical sheet at r = 2 m is enclosed; the sheets at 4 m and 5 m lie outside. Gauss' law gives D(r) = σa/r = 5×2/3 = 10/3 in the radial direction.

Electric-field intensity is force per unit positive test charge. Electric fields obey superposition because electrostatics is linear with respect to source charge in a fixed medium. Key relation: E=F/q; E=Q/(4πεr²) r_hat.

Exam focus: Distance enters as r² and medium enters through ε. Common trap: Do not omit permittivity when comparing different media.

The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles. Key relation: E=−∇V; ΔV=−∫E·dl.

Exam focus: Potential is scalar; electric field is vector. Common trap: Do not assign a direction to electric potential.

Electromagnetic boundary conditions come from Maxwell’s integral equations applied to an infinitesimal loop or pillbox at an interface. They tell you which field components are continuous and which can jump because of surface sources. Key relation: n×(E2−E1)=0 (standard no magnetic surface current); n·(D2−D1)=ρs; n×(H2−H1)=K; n·(B2−B1)=0.

Exam focus: Surface charge affects normal D; surface current affects tangential H. Common trap: Mixing E/D and H/B continuity conditions.

At any point, the electric-field vector points along the tangent to the electric-field line at that point. The arrow direction is the direction in which a positive test charge would experience force.

Gauss's law states that net electric flux through any closed surface is determined by enclosed charge. The flux result depends on enclosed charge, not the geometrical shape of the chosen closed surface. Key relation: ∮D·dS=Q_enclosed; in a uniform medium ∮E·dS=Q_enclosed/ε.

Exam focus: Gauss law is always true; easy field calculation needs symmetry. Common trap: Do not claim every arbitrary charge distribution is easy to solve with Gauss law.

Conduction current density is related to electric field by the point form of Ohm’s law: J = σE = E/ρ. With E = 5 and resistivity ρ = 4.5, the current density is 5/4.5 ≈ 1.11 in the corresponding current-density units.

Bound charges created by polarization oppose the applied field inside the material and increase capacitance for a fixed geometry. Relative permittivity is the ratio ε/ε0 and is at least unity for ordinary passive dielectrics in elementary electrostatics. Key relation: C=εA/d=ε_r ε₀A/d.

Exam focus: Higher permittivity raises capacitance; it does not do so by increasing the internal electric field. Common trap: Do not confuse increased capacitance with increased field strength.

Its characteristic impedance is set by those per-unit-length parameters and frequency, not by line length. A mismatch between load and characteristic impedance causes reflected waves and standing-wave patterns. Key relation: Z₀=√((R+jωL)/(G+jωC)); Γ=(Z_L−Z₀)/(Z_L+Z₀).

Exam focus: Match ZL to Z0 to eliminate reflection. Common trap: Characteristic impedance is not the same as total line impedance.

Using the given constant electric-field magnitude 2 and current density J = x² over x=0 to 1, power is the integral of E·J: ∫₀¹2x²dx = 2/3.

A plane electromagnetic wave can propagate through vacuum without a material medium. In a homogeneous lossless medium, wave speed and intrinsic impedance are set by permittivity and permeability; in free space they reduce to c and about 377 ohms. Key relation: v=1/√(με); η=√(μ/ε); in free space c≈3×10^8 m/s and η0≈377 Ω.

Exam focus: Remember the orthogonal E-H-propagation triad. Common trap: In the elementary nondispersive model, wave speed is not set by frequency.

A plane electromagnetic wave can propagate through vacuum without a material medium. In a homogeneous lossless medium, wave speed and intrinsic impedance are set by permittivity and permeability; in free space they reduce to c and about 377 ohms. Key relation: v=1/√(με); η=√(μ/ε); in free space c≈3×10^8 m/s and η0≈377 Ω.

Exam focus: Remember the orthogonal E-H-propagation triad. Common trap: In the elementary nondispersive model, wave speed is not set by frequency.

The Poynting vector gives electromagnetic power-flow density and points in the direction of energy transport for a propagating wave. It is the cross product of electric and magnetic fields. Key relation: S=E×H [W/m²].

Exam focus: Cross E with H to get energy-flow direction. Common trap: V/m is electric-field unit, not Poynting-vector unit.

For A = x i + y j + z k, each component depends only on its corresponding coordinate. All cross-partial derivatives in ∇×A are zero, so the field is curl-free (irrotational).

The surface z=0 with 30°<φ<60° is a sector-shaped region of the xy-plane between two rays. Because neither φ=0° nor φ=90° is included, it contains neither the positive x-axis nor positive y-axis, while the radial extent is not bounded by the angular condition. The statement combination is option D.

A solenoidal vector field is divergence-free: ∇·A = 0. Physically, it has no net source or sink within the region.

Use Gauss' divergence theorem. For F = 3x i + 2y j, ∇·F = 3 + 2 = 5. The sphere x²+y²+z²=9 has radius 3 and volume 36π, so the outward flux is 5×36π = 180π.

The three basic vector differential operators have distinct outputs: gradient maps scalar→vector, divergence maps vector→scalar, and curl maps vector→vector. Remembering input/output type is often enough to eliminate distractors. Key relation: grad φ=∇φ; div A=∇·A; curl A=∇×A; ∮_S A·dS = ∫_V (∇·A)dV.

Exam focus: Use the mnemonic: Grad grows a scalar into a vector; Div gives a scalar; Curl gives a vector. Common trap: Calling gradient a scalar because the original field is scalar.

A diamagnetic material has permeability slightly below that of free space, equivalently relative permeability μr slightly less than 1. It develops a weak magnetization opposite to the applied field.

Diamagnetic substances have a small negative susceptibility, so μr = 1 + χm is slightly less than 1.

Ampere's circuital law relates circulation of magnetic field to enclosed current for magnetostatic cases. Symmetric geometries such as an infinite straight conductor or long solenoid make the integral law especially useful. Key relation: ∮H·dl=I_enclosed (magnetostatic); ∮H·dl=I_c+d/dt∫D·dS (general form).

Exam focus: For time-varying fields, use the Ampere-Maxwell form. Common trap: Saying Ampere's law has no time-varying extension is incomplete.

Magnetic flux density is solenoidal because ∇·B=0—there are no magnetic monopoles. A static magnetic field is not generally conservative in regions containing current, since Ampère’s law gives ∇×H=J. Therefore statement 1 is true and statement 2 is false, matching option A.

The continuity equation follows by taking the divergence of the Ampère-Maxwell law and using Gauss' law. This yields ∇·J = -∂ρv/∂t.

Maxwell's equations unify electric and magnetic fields. Maxwell added displacement current to Ampere's law, showing that a time-varying electric field acts as a source of magnetic field. Key relation: ∇×H=J+∂D/∂t; ∇×E=−∂B/∂t.

Exam focus: Changing E produces H; changing B produces E. Common trap: Maxwell's equations are not limited to static fields.

Faraday's law gives e = -dΦ/dt. For Φ = 3 sin t + 5 cos t, dΦ/dt = 3 cos t - 5 sin t, so e = -3 cos t + 5 sin t.