Contents
Tangent, Normal & Binormal of Space Curves
Differentials in cylindrical & Spherical System
Introduction to Boundary Conditions
Parallel polarization (TM Polarization)
Perpendicular polarization (TE Polarization)
Dot Product 


Commutative 
Cross Product 


Noncommutative 
Gradient 


· Gradients works on scalar functions. · Gradient of a function gives a vector · It is rate of change of a function (with information about directions) 
Divergence 


· Divergence works on vector functions. · Divergence of a functions gives a scalar · It is rate of change of a function (without information about directions) 
Curl 


· Curl works on vector functions. · Curl of a functions gives a vector. · It is measure of rotational ability of a function (with information about directions) 
Directional Derivative of function F along 



Directional Derivative of function F along at a point P( 



Triple Product 
=
The best way to remember this rule is by using outermiddleinner terms





Consider two vectors as shown in the figure. The projections of on is given below. 


Parallel Projection : Vector Component of in the direction of



Normal Projection : Vector Component of perpendicular to 

Since

Given a vector another vector parallel or perpendicular to it 

Parallel to 
where m=integer 
Perpendicular to 

Given a space curve defined by the vector then the Tangent vectors to any point on the space curve is 

Normal vector to any point on the curve 

Electric field due to a point charge with position vector at any point with position vector


Electric field due to line charge distribution


Electric field due to surface charge distribution 

Cylindrical Coordinate Systems 

Azimuthal Angle 
Spherical Coordinate System 

Polar Angle Azimuthal Angle

Cylindrical Cartesian


Cartesian Cylindrical 

Spherical Cartesian 

Cartesian Spherical 

Spherical Cylindrical 

Cylindrical Spherical 

http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
Coordinate System 
Elemental Surface area 
Cylindrical System
Surface area of the elemental volume 
Note: in radians. 
Spherical System
Surface area of the elemental volume 

Coordinate System 
Elemental Volume 
Cylindrical 

Spherical 

Coordinate System 
Elemental Arc Length 
Scale Factors 
Cylindrical 


Spherical 


Given a space curve as shown in the figure the correspondingtangent vector , normal vector and
binormal unit vector


Parametric Equation of a line from to
;

Vector Form 
Parametric Form 
Equation of a line parallel to vector and passing through the point 


Equation of a line passing through the points and 
Here the range of is 
Here the range of is 
Equation of a plane perpendicular to vector and passing through the point 

where




Orthogonal 
Cylindrical 







MAXWELLS EQUATION 
Derivative Form 
Integral Form 
Using phasors and complex permittivity 
Gauss's Theorem 



Gauss's Theorem (in magnetism) 



Ampere's Law 



Faraday's Law 



In static case 
Electrostatics/ Magneto statics 
Gauss's Theorem 

Gauss's Theorem (in magnetism) 

Ampere's Law 

Faraday's Law 
; 
Magnetic Field Intensity 

Electric field intensity 

Electric potential 

Magnetic potential 

Continuity Equation 

Laplace's Equation 

Poisson's Equation 
(electrostatic) (magneto statics) 
Ohm's Point Law 

Conduction Current density 

Displacement Current density 

Intrinsic Impedance 

Velocity in any media 

Relation between and 

The three constitutive parameter of a medium are
Complex permittivity is defined as


Properties of the medium 
Wave Equation 
Propagation Constant 
Charge free medium 


Charge free and Lossless medium



General wave equations :
For a uniform plane in xy Click here for derivation


Set of wave equations Click here for derivation obtained from general wave equations


The general solution of the wave equation is of the form
Assuming that has component only along xdirection and is travelling along + zdirection, we have
Use right hand rule for direction

Electric fields
Magnetic fields
Tangential components
Normal component
Tangential components
Normal component

SNELL'S LAW
Refractive index of a medium ( = 

Electromagnetic Reflection and Transmission for Normal Incidence
· Transmission coefficient
· Reflection coefficient
·
· Ratio of powers . Replace with complex impedance if the medium is lossy (Electric field is tangential to the boundary between the two media. Polarization has no effect on electric field at normal incidence. 

It is a plane containing 1) direction of propagation and 2) normal to the boundary between the two surfaces.
Electric field is parallel to the plane of incidence.
Electric filed is normal to the plane of incidence
PARALLEL POLARIZATION 
PERPENDICULAR POLARIZATION 






LINEAR 


CIRCULAR 
Since


ELLIPTICAL 
=
If χ is +ve=LHCP If χ is −ve=RHCP

· lies between · 2 values of satisfies the above equation. · If select · If select · lies between

Faradays Law 

Flux 
is the magnetic flux associated with currents / materials
