RAJALAKSHMI ENGINEERING COLLEGE

THADALAM, CHENNAI

EC2253 – ELECTROMAGNETIC FIELDS

TWO QUESTION AND ANSWER

UNIT 1

1. Define scalar and vector.

A quantity that is characterized only by magnitude is called a scalar.
A quantity that is characterized both by magnitude and direction is called a vector.

2. Define gradient.
The gradient of any scalar function is the maximum space rate of change of that function. If scalar V represents
electric potential, V represents potential gradient.
V= . This operation is called gradient.

3. Define divergence.
The divergence of a vector ‘A’ at any point is defined as the limit of its surface integrated per unit volume as the
volume enclosed by the surface shrinks to zero.
.V = ds .A =

4. Define curl.
The curl of a vector ‘A’ at any point is defined as the limit of its surface integral of its cross product with
normal over a closed surface per unit volume shrinks to zero.
|curl A| =

5. Define divergence theorem.

The volume integral of the divergence of a vector field over a volume is equal to the surface integral of the
normal component of this vector over the surface bounding the volume. =

6. State stokes theorem.

The line integral of a vector around a closed path is equal to the surface integral of the normal component of
its curl over any surface bounded by the path.

dl = ( x H) ds

7. State coulombs law.

Coulombs law states that the force between any two point charges is directly proportional to the product of
their magnitudes and inversely proportional to the square of the distance between them. It is directed along
the line joining the two charges. F=Q1Q2 / 4πεr2

8. State Gauss law. Under what condition in Gauss’s law especially useful in determining the Electric field
intensity of a charge distribution.
The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
Charge distribution is symmetrical the Gauss’s law is useful in determining the Electric field intensity of a
charge distribution.

9. Define electric flux and electric flux density.

The lines of electric force are electric flux. Electric flux density is defined as electric flux per unit area.
10. Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.

E =F/ Q =Q/4πεr2 V/m

11. Name few applications of Gauss law in electrostatics.

Gauss law is applied to find the electric field intensity from a closed surface. e.g) Electric field can be
determined for shell, two concentric shell or cylinders etc.

12. Define linear charge density.

Linear charge density is defined as the charge per unit length.

13. Define potential difference.

Potential difference is defined as the work done in moving a unit positive charge from one point to another
point in an electric field.

14. Define electric scalar potential.

Potential at any point is defined as the work done in moving a unit positive charge from infinity to that point in
an electric field. V=Q / 4πεr Volts

15. Give the relationship between potential gradient and electric field.
E= - V

16. Define dipole and dipole moment.

Dipole or electric dipole is nothing but two equal and opposite point charges are separated by a very small
distance. The product of electric charge and distance n know as dipole moment. It is denoted by m where Q is
the charge l is the length. m=Q.l

17. Find the gradient of scalar system t= x2 y + ez at point P(1, 5, -2).

= (x2 y + ez)
=2xyi +x2j + ezk = 10i + j + e-2k

18. Define volume charge density.

Volume charge density is defined as, the charge per unit volume.
Pe =
UNIT 2
UNIT 3
 UNIT 4

1. Define Poynting vector?

The cross product of electric field and magnetic intensity vector is defined as pointing vector
P=ExH (or)
Poynting vector gives the magnitude as well as the direction in which power flows in time varying
electromagnetic fields.
2. Determine emf developed about the path r = 0.5, z = 0 and t = 0. If B = 0.01 sin 377 t.
e = - dф / dt = - d / dt (B.A)
= -A d / dt (0.01 sin 377 t)
e t=0 = -2.96V
3. Write down Maxwell’s equation derived from Faraday’s law?
∫ E. dl = -∫ ∫ (∂B / ∂t ) ds ---- Integral form
Del cross E = - ∂B / ∂t --- Differential form
4. What is displacement current and conduction current?
The current through a capacitor is called displacement current. It is denoted as I D.
ID = dQ / dt
The current through a conductor is called conduction current. It is denoted as I C.
IC = V / R
5. Brief about the ampere’s circuital law for a in integral form.
Ampere’s law states that the line integral of magnetic field intensity H on any closed path is equal to the current
enclosed by the path
∫ H. dl = I
∫ H. dl = ∫ ∫ {J + ∂D / ∂t} ds
6. State Faraday’s law for a moving charge in a constant magnetic field.
Faraday’s law states that the electromagnetic force (mmf) induced in a circuit is equal to the rate of decrease of
the magnetic flux linkage the circuit.
v = - dф / dt
7. Write down Maxwell’s equation in integral form?
(i) ∫ H. dl = ∫ ∫ {J + ∂D / ∂t} ds
(ii) ∫ E. dl = -∫ ∫ (∂B / ∂t ) ds
(iii) ∫∫ D. ds = ∫∫∫ ρ. dv
(iv) ∫∫ B. ds = 0
8. Write down Maxwell’s equation in point form?
▼ x H = J + ∂D / ∂t ▼.D = ρ
▼ x E = -∂B / ∂t ▼.B = 0
9. State Poynting Theorem?
Poynting Theorem states that the net power flowing out of a volume v is equal to the time rate of decrease in
the energy stored within a volume v minus the conduction losses.
∫ (E x H). ds = - ∂ / ∂t ∫ (½ εE2 +½ μH2) dv - ∫ζ E2 dv.
10. Mention significance of displacement current density and conduction current density?
Displacement current density = JD =∂D / ∂t =ε∂E / ∂t
Conduction current density = Jc = ζE
11. Discuss the condition under which conduction current is equal to displacement current?
In a conductor conductivity ζ goes to zero means it act as a dielectric and corresponding current is displacement
current.
12. Brief about complex Poynting vector?
The complex Poynting vector is given by, P = ½ (E x H)
The product of E and H is vector product. The mutually perpendicular components E and H, contribute to the
power flow. This power flow is directed along the normal to the plane containing E and H.
13. Write Helmholtz’s equation.
▼2E – γ2E =0
Where γ =[ j μω(ζ + j ωε)]1/2
 Unit 5
1. Define a wave?
If a physical phenomenon that occurs at one place at a given time is reproduced at other places at later times, the
time delay being proportional to the space separation from the first location, then the group of phenomena
constitute a wave.
2. Define the term intrinsic impedance of free space with its value?
It is the ratio of electric field to magnetic field or It is the ratio of square root of permeability to permittivity of
the medium. η = E /H = √(μ0 / ω0) =377 ohms

3. Mention properties of uniform plane wave?

1. At every point in space, the electric field E and magnetic field H are perpendicular to each other and to the
direction of the travel.
2. The fields are vary harmonically with time and at the same frequency, everywhere in space.
3. Each field has the same direction, magnitude and phase at every point in any plane perpendicular to the
direction of wave travel.
4. What is meant by skin effect or skin depth or depth of penetration?
Skin depth is defined as that of depth in which the wave has been attenuated to 1/e or 37% of its original value.
δ =1/ α =√2/(jωζ) = for good conductor.
5. Explain Polarization?
Polarization is defined as the time varying nature of the electric field vector at some fixed point in space.
(a) If x and y component of electric field Ex and Ey are present and are in phase, the resultant field has a
direction at an angle of tan-1(Ey/Ex) and if the phase angle is constant with time, the wave is to be linearly
polarized.
(b) If x and y component of electric field Ex and Ey have different amplitude and 90ο phase difference, the
locus of the resultant electric field E is a circle and wave is to be circularly polarized.
(c) If x and y component of electric field Ex and Ey have different amplitude and 90ο phase difference, the
locus of the resultant electric field E is a ellipse and wave is to be elliptically polarized.
6. What is Brewster Angle?
Brewster Angle is an incident angle at which there is no reflected wave for parallely polarized wave. θ = tan-1 √
ε2/ε1 where, ε1 = dielectric constant of medium 1, ε2 = dielectric constant of medium 2

7. Write down the wave equation for E and H in free space.

2 2
H– μ ε E– μ ε

8. Define propagation constant.

Propagation constant is a complex number γ =α +jβ where α is attenuation constant
β is phase constant γ = √jωµ (σ+jωε)

9. Define loss tangent.

Loss tangent is the ratio of the magnitude of conduction to displacement current density of the medium.

10. Define reflection coefficients and transmission coefficients

Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.
Transmission coefficient is defined as ratio of the magnitude of the transmitted field to that of incident field.

11. What are uniform plane waves?

Electromagnetic waves which consist of electric and magnetic fields that are perpendicular to each other and
to the direction of propagation and are uniform in plane. Perpendicular to the direction of propagation are
known as uniform plane waves.

12. State Snell’s law.

When a wave is travelling from one medium to another medium, the angle of incidence is related to angle of

reflection as follows. = Where, θi is angle of incidence, θt is angle refraction