Posts

Electric Field Intensity Due To a Finite Line Charge - Field Theory.

- Consider a line charge with uniform charge density ρL extending from + a to – a along the z- axis.


- Charge element dQ associated with the element dl of the line is

 dQ = ρL dl = ρL dz



- From the diagram it’s clear that the Electric field intensity has two components i.e. Eρ and Ez.


- If we move around the line charge and if we vary ρ, while keeping φ and z constant, it is expected that the field would become weaker as ρ increases.


- No element of charge produces a φ component i.e. Eφ is equal to zero.


- Hence Electric field intensity at point P has only two component one along the ρ and the other along the z direction.


- However the contribution due to Ez component by the elements of charge will be canceled because the same are at equal distances above and below the point at which the field is to be determined.


(For Example: If a charge element is present at + 4az and another charge element at - 4az, then the z component due to the two mentioned charge element at the point P will…

Eletromagnetics - Questions With Answers (Short Notes)

Image
1. Define A Uniform Plane Wave.

Answer: In an uniform plane wave the electric and magnetic field vectors both lie in a plane and all such planes are parallel to each other. Also the amplitude and phase of vectors E and H are constant over the planes & they are always normal to the direction pf propagation.


2. State Gauss Divergence Theorem.

Answer: This theorem states that the net flux of a vector field F over any closed surface S is equal to the volume integral of the divergence of that vector field over the volume enclosed by the surface S.

Mathematically it is expressed as:

3. State Stoke’s Theorem.

Answer: This theorem states that the line integral of vector field A around the closed curve forming the periphery of any surface S is equal to surface integral of the curl of that vector field taken over surface S bound by the curve forming periphery of the surface.

Mathematically it is expressed as:

4. What Do You Understand By Displacement Current?

Answer: Maxwell suggested that it is n…

Magnetic Forces, Materials, and Devices - Questions With Answers (Short Notes)

Image
01. State Three Ways In Which Forces Due To Magnetic Fields Can Be Experienced?

Answer: There are at least three ways in which force due to magnetic fields can be experienced. The
force can be

due to a moving charged particle in a magnetic field.on a current element in an external magnetic field.between two current elements.
02. State The Lorentz Force Equation?

Answer: The Lorentz force equation relates the force acting on a particle with charge Q in the presence of EM fields. It expresses the fundamental law relating EM to mechanics.

F = Q(E + u * B) = m ( du/dt)
Based on the Lorentz force law, the force experienced by a current element Idl in a magnetic field B is
dF = I dl * B
From this, the magnetic field B is defined as the force per unit current element.


03. Define Magnetic Torque?

Answer: The torque T (or mechanical moment of force) on the loop is the vector product of the force F and iho moment arm r.

T = r X F and magnetic torque is measured in Newton-meters (N • m).

Magnetic torq…

Electric Fields In Material Space - Questions With Answers (Short Notes)

01. How Can Materials Be Classified In Terms Of Their Electrical Properties?

Answer:  Materials can be classified roughly as conductors (σ >> 1, εr = 1) and dielectrics (σ << 1, εr ≥ 1) in terms of their electrical properties σ and εr where σ is the conductivity and εr is the dielectric constant or relative permittivity.

A material with high conductivity ( σ >> 1) is referred to as a metal whereas one with low conductivity (σ << 1) is referred to as an insulator. A material whose conductivity lies somewhere between those of metals and insulators is called a semiconductor.


02. Define Superconductor?

Answer: The conductivity of metals generally increases with decrease in temperature. At temperatures near absolute zero (T = 0°K), some conductors exhibit infinite conductivity and are called superconductors. Lead and aluminum are typical examples of such metals.


03. Why Conductor Is Called An Equipotential Body? What Are Perfect Conductors?

Answer: A conductor is called …

Part I - Electric & Magnetic Field In Material Space - Questions With Answers (Short Notes)

Image
1. What Do You Mean By Dielectric Constant Of A Material ?

Answer: Dielectric constant (k) or relative permittivity (εr) is defined as the ratio of capacitance of a capacitor with dielectric to the capacitance of same capacitor without dielectric. It generally describes the ability of a material to polarize and store a charge.

Mathematically, k or εr = C/C0 .

[Since C = q/V, we have εr = E0/E = V0/V = ε/εr ].


2. Define Dielectric Medium.

Answer: Dielectric is a material in which energy can be stored by the polarization of the molecules. It is a material that increases the capacitance or charge storage ability of a capacitor. Ideally, a dielectric is an insulator and does not contain free charge. However, in the presence of external field it exhibits a relative displacement of opposite bound charges and hence the polarization of the medium. Due to polarization induced surface charges tend to weaken the original field within the dielectric.

[The resultant field in the presence of dielectric…

ElectroStatics - Questions With Answers (Short Notes)

Image
1. State Stokes Theorem.

Answer: 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

∫ H.dl = ∫ ∫ ( ∆ x H ) ds
where, H is the Magnetic field intensity

2. State The Condition For The Vector F To Be Solenoidal.

Answer:
∆ . F = 0
where, F = A i + B i + C i

3. State The Condition For The Vector F To Be Irrotational.

Answer:

∆ x F = 0 where, F = A i + B i + C i

4. Give The Relationship Between Potential Gradient and Electric Field.

Answer: 
E = - ∆V
where, E represents Electric Field Intensity and V represents Electric Potential

5. What Is The Physical Significance Of div D ?

Answer: The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.

6. What Are The Sources Of Electric Field & Magnetic Field?

Answer: Stationary charges produce electric field that are constant in time, hence the term electrostatics. Movin…

State The Difference Between Conduction & Displacement Current?

Image
The differences between Conduction Current and displacement current are:

1. Conduction current obeys ohm's law as V = (I / R) but displacement current does not obey ohm's law.

2. Conduction current density is represented by

 whereas displacement current density is given by

3. Conduction current is the actual current whereas displacement current is the apparent current produced by time varying electric field.

Antenna Theory - Solved Numerical's / Problems - ElectroMagnetic Theory...

Image
1) An electric field strength of 10 µV/m is to be measured at an observation point θ = π/2, 500 km from a λ/4 monopole antenna operating in air at 50 MHz.
(a) What is the length of the dipole?(b) Calculate the current that must be fed to the antenna.(c) Find the average power radiated by the antenna.(d) If a transmission line with Zo = 75 Ω is connected to the antenna, determine the standing wave ratio. --- For Solution CLICK HERE.

2) Calculate the directivity of
The Hertzian Monopole.The quarter-wave Monopole.  --- For Solution CLICK HERE.
3) A certain antenna with an efficiency of 95% has maximum radiation intensity of 0.5 W/sr. Calculate its directivity when
(a) The input power is 0.4 W
(b) The radiated power is 0.3 W  
 --- For Solution CLICK HERE.


4) Evaluate the directivity of an antenna with normalized radiation intensity
 --- For Solution CLICK HERE.

5) Determine the maximum effective area of a Hertzian dipole of length 10 cm operating at 10 MHz. If the antenna receives 3 µW of power, w…

Vector Analysis & Electrostatics - Index / Sitemap.

INDEX
Vector analysis is a mathematical tool with which electromagnetic (EM) concepts are most conveniently expressed. It's important to learn its rules and techniques first applying it.

VECTOR ALGEBRA:

- Scalars and Vectors.

- Unit Vectors.

- Position and Distance Vectors.

- Vector Multiplication.

- Components Of a Vector.

- Numericals / Solved Examples.


COORDINATE SYSTEMS & TRANSFORMATION:

In general, the physical quantities in ElectroMagnetics are functions of space and time. In order to describe the spatial variations of the quantities, its important to define all points uniquely in space in a suitable manner. This requires using an appropriate coordinate system. Hence its very important to understand the coordinate system first. 

- Introduction To Coordinate System.

- Cartesian Coordinate System / Rectangular Coordinate System (x, y, z).

- Differential Analysis Of Cartesian Coordinate System.

- Circular Cylindrical Coordinate System (ρ, φ, z).

- Differential Analysis Of Cylindrical Coo…