Dot Product			Commutative
Cross Product			Non-commutative
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(

Basics – 1

Triple Product

The best way to remember this rule is by using outer-middle-inner terms

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

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B

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

Electrostatic Basics

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

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;:- -

Electric field due to line charge distribution

Electric field due to surface charge distribution

Mangnetostatics Basics

Coordiante systems

Cylindrical Coordinate Systems

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z
Cylindrical System
Z P(r,O,z)
,
- I
9
rstne
— /
1

Azimuthal Angle

Spherical Coordinate System

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z
Spherical System
r sinO sin4

Polar Angle

Azimuthal Angle

Transformation Matrix

Cylindrical Cartesian
Cartesian Cylindrical
Spherical Cartesian
Cartesian Spherical
Spherical Cylindrical
Cylindrical Spherical

http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates

Volume & Surface Areas

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

Tangent, Normal & Bi-normal of Space Curves

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

bi-normal unit vector

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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

Differentials in cylindrical & Spherical System


Orthogonal	Cylindrical

Maxwell's Equation

MAXWELLS EQUATION	Derivative Form	Integral Form	Using phasors and complex permittivity
Gauss's Theorem		click for derivation
Gauss's Theorem (in magnetism)
Ampere's Law		click for derivation
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

Complex Permittivity

The three constitutive parameter of a medium are

Complex permittivity is defined as

Wave Equation

Properties of the medium	Wave Equation	Propagation Constant
Charge free medium
Charge free and Loss-less medium
General wave equations : For a uniform plane in x-y Click here for derivation

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

Solution to Wave Equations

The general solution of the wave equation is of the form

Assuming that has component only along x-direction and is travelling along + z-direction, we have

Use right hand rule for direction

Equation representing Wave

Introduction to Boundary Conditions

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.