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EE 222

ELECTROMAGNETIC

THEORY

Yasa Ekşioğlu Özok

Chapters will be covered in the course:

• Electromagnetic model
• Vector Analysis
• Static Electric Fields
• Solution of Electrostatic Problems
• Steady Electric Currents
• Static Magnetic Fields

VECTOR ANALYSIS

• Some of the scalar quantities in electromagnetics are: current,

charge, and energy.

• Electric and Magnetic field intensities are vectors.

The main topics of the chapter:

• Vector Algebra; addition, substraction, multiplication of vectors.
• Orthogonal coordinate systems; cartesian, cyclindirical and

spherical coordinates

• Vector calculus;differentation and integration of vectors, gradient,

divergence and curl operations.

• Electric field intensity discuss the effects of stationary

electric charges

• Electric field displacement is useful when we study of

electric fied in media

• Magnetic flux density is the only vector needed in

discussing effects of steady electric currents

• Magnetic field intensity study of magnetic field in

media

• We have positive scalar ‘n’ and it changes the

magnitude of vector ‘A’ by multiplication

𝑛𝐴 = 𝑎(𝑛𝐴) direction of the vector is same

SCALAR (DOT) Product

PRODUCT of VECTORS

𝐴. 𝐵 = 𝐴 𝐵 cos 𝜃𝐴𝐵

Multiplication of same vectors with each other

Vector (CROSS) Product

• 𝐴 × 𝐵 = 𝑎𝑛 𝐴 𝐵 sin 𝜃𝐴𝐵

Product of 3 VECTORS

Orthogonal Coordinate Systems

• In order to determine the electric field at a certain point in

space, we need to describe the position of the source and the location of this point in a coordinate system.

• In 3 dimensional systems we use x1,x2,x3 or x,y,z (in

cartesian or rectangular coordinates)

• When these 3 coordinates are perpendicular to each

other we have an Orthogonal Coordinate System.

(Base vectors-unit vectors)

𝐶 ∙ 𝐴 × 𝐵 =?

Line, Surface, and Volume Integrals

• In electrodynamics we encounter several different kinds of integrals,

among which the most important are line (or path) integrals, surface

integrals (or flux), and volume integrals.

line (or path) integrals:

𝑏

𝑎

𝑣: vector function, 𝑑𝑙: infinitesimal displacement vector

If the path forms a closed loop ( b =a ), we denote the integral as

surface integrals:

𝑣: vector function, 𝑑𝑠: infinitesimal patch of area with direction perpendicular to the surface

(closed loop)

where T is a scalar function and 𝑑𝑣 is an infinitesimal volume element.

volume integrals:

Orthogonal coordinates the differential area 𝑑𝑠 1 normal to the unit vector 𝑎𝑢

Dot product of vector A and B

Vector product of vector A and B

Expressions for differential length, diffferential area and differential volume

CYLINDIRICAL COORDINATES

is the intersection of a circular cylindirical surface

Base vectors by considering right-hand rule

vector A in cyclindirical coordinates

Expressions for differential length, diffferential area and differential volume

Cartesian coordinates in

terms of cyclindirical

coordinates