1 $If is a scalar function, what does represent?$

A.

Divergence of

B.

Laplacian of

C.

Gradient of

D.

Curl of

2 $Which of the following represents the physical significance of the divergence of a vector field?$

A.

The direction of maximum increase

B.

The net outflow of flux per unit volume

C.

The rotational effect of the field

D.

The circulation of the field around a loop

3 $A vector field is said to be solenoidal if:$

A.

B.

C.

D.

4 $If a vector field is irrotational (conservative), which of the following is true?$

A.

B.

C.

The field cannot be expressed as a gradient

D.

5 $What is the value of for any twice-differentiable vector field ?$

A.

B.

It depends on the coordinate system

C.

1

D.

0

6 $Gauss's Divergence Theorem relates a surface integral to a:$

A.

Curl

B.

Line integral

C.

Volume integral

D.

Gradient

7 $Stokes' Theorem relates a line integral over a closed path to a:$

A.

Surface integral over a closed surface

B.

Gradient of the field

C.

Volume integral enclosed by the path

D.

Surface integral over an open surface bounded by the path

8 $Which mathematical equation represents Poisson's Equation in electrostatics?$

A.

B.

C.

D.

9 $Laplace's equation is a special case of Poisson's equation where:$

A.

The permittivity is infinite

B.

The field is time-varying

C.

The region is charge-free ()

D.

The magnetic field is zero

10 $The Equation of Continuity is a mathematical statement of the conservation of:$

A.

Mass

B.

Momentum

C.

Energy

D.

Charge

11 $The differential form of the continuity equation is given by:$

A.

B.

C.

D.

12 $For steady currents (DC), the continuity equation reduces to:$

A.

B.

C.

D.

13 $Which of Maxwell's equations is essentially Gauss's Law for Electrostatics ?$

A.

B.

C.

D.

14 $The equation implies the non-existence of:$

A.

Displacement current

B.

Electric dipoles

C.

Magnetic monopoles

D.

Static magnetic fields

15 $Maxwell's third equation,, is the differential form of:$

A.

Gauss's Law

B.

Lenz's Law only

C.

Faraday's Law of Electromagnetic Induction

D.

Ampere's Law

16 $In Ampere's Circuital Law, the term added by Maxwell to correct the law for time-varying fields is called:$

A.

Displacement current

B.

Conduction current

C.

Eddy current

D.

Convection current

17 $The formula for displacement current density is:$

A.

B.

C.

D.

18 $Maxwell's modification of Ampere's Law is written as:$

A.

B.

C.

D.

19 $Displacement current arises due to:$

A.

Time-varying electric field

B.

Flow of electrons in a wire

C.

Flow of ions in a solution

D.

Steady magnetic field

20 $In free space (vacuum), the constitutive relation between and is:$

A.

B.

C.

D.

21 $The integral form of Maxwell's equation is:$

A.

B.

C.

D.

22 $The physical significance of in electrostatics is:$

A.

The electric field is non-conservative

B.

Magnetic monopoles exist

C.

The electric field is conservative

D.

There is a time-varying magnetic field

23 $Which of the following is the correct unit for Electric Flux Density ()?$

A.

Volts/meter ()

B.

Coulombs/meter squared ()

C.

Tesla ()

D.

Coulombs ()

24 $For a perfect dielectric, the conduction current density is:$

A.

Negative

B.

Equal to displacement current

C.

Infinite

D.

Zero

25 $The minus sign in Faraday's Law () represents:$

A.

Lenz's Law

B.

Gauss's Law

C.

Ampere's Law

D.

Ohm's Law

26 $Which vector identity is used to prove that magnetic monopoles do not exist () given that ?$

A.

Divergence of a Curl is zero

B.

Curl of a Curl is Gradient of Divergence minus Laplacian

C.

Divergence of a Gradient is the Laplacian

D.

Curl of a Gradient is zero

27 $Ampere's Circuital Law fails for time-varying fields because:$

A.

It violates conservation of energy

B.

It only applies to vacuum

C.

Magnetic fields cannot vary with time

D.

It violates conservation of charge (Continuity Equation)

28 $The ratio of conduction current density to displacement current density () is given by:$

A.

B.

C.

D.

29 $In the integral form of Maxwell's 4th equation, the term represents:$

A.

Conduction Current ()

B.

Magnetic Flux

C.

Electric Potential

D.

Displacement Current ()

30 $For a static magnetic field, which of the following is true?$

A.

B.

C.

D.

31 $Which theorem converts a volume integral of a scalar function's gradient into a surface integral?$

A.

Stokes' Theorem

B.

Green's Theorem

C.

Gradient Theorem (Generalized)

D.

Gauss's Divergence Theorem

32 $The operator is called the:$

A.

Hamiltonian

B.

Div-Curl

C.

Gradient

D.

Laplacian

33 $In Maxwell's equations, . Here represents:$

A.

Permittivity

B.

Conductivity

C.

Susceptibility

D.

Permeability

34 $If, what is ?$

A.

B.

0

C.

3

D.

1

35 $If, what is ?$

A.

3

B.

C.

0

D.

36 $The displacement current is equal to the conduction current in a parallel plate capacitor when:$

A.

The capacitor is being charged

B.

Always (in terms of circuit continuity)

C.

The capacitor is fully charged

D.

The dielectric is perfect

37 $Which of the following is NOT a vector field?$

A.

Current Density

B.

Electric Field Intensity

C.

Magnetic Flux Density

D.

Electric Potential

38 $Maxwell's equations predict that electromagnetic waves travel in free space with a speed of:$

A.

B.

C.

D.

39 $What is the physical interpretation of pointing in a specific direction?$

A.

It points in the direction of constant potential

B.

It points in the direction of the greatest rate of increase of V

C.

It points in the direction of the greatest rate of decrease of V

D.

It is perpendicular to the electric field

40 $The total current passing through a closed surface is zero implies:$

A.

Charge inside is conserved

B.

C.

Kirchhoff's Current Law applies to the enclosed volume

D.

The displacement current cancels the conduction current

41 $Which quantity is conserved in the continuity equation?$

A.

Charge

B.

Power

C.

Flux

D.

Voltage

42 $In the derivation of the wave equation from Maxwell's equations for free space, the charge density and current density are set to:$

A.

Zero

B.

Unity

C.

Variable

D.

Infinity

43 $The curl of the gradient of electric potential is:$

A.

Zero

B.

Electric Flux

C.

Charge Density

D.

Electric Field

44 $Stokes' Theorem is applicable to:$

A.

Only scalar fields

B.

Only time-varying fields

C.

Only vector fields

D.

Both scalar and vector fields

45 $The region in which Laplace's equation is valid is called:$

A.

Sink region

B.

Source region

C.

Charge-free region

D.

Conducting region

46 $If the divergence of a vector field is positive at a point, that point acts as a:$

A.

Sink

B.

Source

C.

Vortex

D.

Saddle point

47 $The electric field is related to the potential by:$

A.

B.

C.

D.

48 $Which of the following equations represents the integral form of Ampere's Law without Maxwell's correction?$

A.

B.

C.

D.

49 $The concept of displacement current is associated with:$

A.

Magnetic field produced by a moving charge

B.

Current in a resistor

C.

Electric field produced by a static charge

D.

Magnetic field produced by a changing electric field

50 $For a vector field, the identity is physically significant because it leads to:$

A.

Conservation of charge

B.

for steady currents

C.

(Magnetic monopoles don't exist)

D.

in electrostatics

Unit 1 - Practice Quiz