Lecture 21 - Basic Laws of Electromagnetics Notes | EduRev

: Lecture 21 - Basic Laws of Electromagnetics Notes | EduRev

 Page 1


 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
   Objectives
   In this course you will learn the following
Gauss's Law
Gauss's Law for Magnetic Flux Density
Page 2


 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
   Objectives
   In this course you will learn the following
Gauss's Law
Gauss's Law for Magnetic Flux Density
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
Gauss's Law
The Gauss's law states that the total outward electric displacement through any closed surface surrounding
charges is equal to the total charge enclosed.
Let us now consider a closed surface  surrounding the charges , ,  as shown in Fig. Then through
an incremental area  on the surface, the outward electric displacement will be . The total electric
displacement can be obtained by integrating over the surface S. Then according to the Gauss's law
Instead of discrete charges , , ...  if there is a continious distribution of charge inside the closed
surface, we have to find total charge by integrating over the enclosed volume. The distributed charges can be
correctly represented by a charge density  which in general is a function of space. The  is the charge per
unit volume having units . The charge in a small volume dV will be . The total charge
enclosed by the volume can be obtained by integrating over the volume V. For distributed charges then
becomes
This is the Gauss law in the integral form
  
The equivalent differential form can be obtained by applying the Divergence theorem to the above eqn.
Substituting and bringing all the terms on the left hand side of the equality sign we get
This is the differential form of the Gauss's law.
Page 3


 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
   Objectives
   In this course you will learn the following
Gauss's Law
Gauss's Law for Magnetic Flux Density
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
Gauss's Law
The Gauss's law states that the total outward electric displacement through any closed surface surrounding
charges is equal to the total charge enclosed.
Let us now consider a closed surface  surrounding the charges , ,  as shown in Fig. Then through
an incremental area  on the surface, the outward electric displacement will be . The total electric
displacement can be obtained by integrating over the surface S. Then according to the Gauss's law
Instead of discrete charges , , ...  if there is a continious distribution of charge inside the closed
surface, we have to find total charge by integrating over the enclosed volume. The distributed charges can be
correctly represented by a charge density  which in general is a function of space. The  is the charge per
unit volume having units . The charge in a small volume dV will be . The total charge
enclosed by the volume can be obtained by integrating over the volume V. For distributed charges then
becomes
This is the Gauss law in the integral form
  
The equivalent differential form can be obtained by applying the Divergence theorem to the above eqn.
Substituting and bringing all the terms on the left hand side of the equality sign we get
This is the differential form of the Gauss's law.
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
 
Gauss's Law for Magnetic Flux Density
The total magnetic flux coming out of a closed surface is equal to the total magnetic charges (poles) inside the surface.
However there are no isolated magnetic monopoles. The magnetic poles are always found in pair with opposite polarity.
As a result, there are always equal number of north and south poles inside any closed surface making net magnetic
charges identically zero inside a volume. The total outward magnetic flux from any closed 
surface therefore must identically be equal to zero. Writing mathematically,
Where B is the magnetic flux density. Applying the Divergence theorem we get
 or
Page 4


 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
   Objectives
   In this course you will learn the following
Gauss's Law
Gauss's Law for Magnetic Flux Density
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
Gauss's Law
The Gauss's law states that the total outward electric displacement through any closed surface surrounding
charges is equal to the total charge enclosed.
Let us now consider a closed surface  surrounding the charges , ,  as shown in Fig. Then through
an incremental area  on the surface, the outward electric displacement will be . The total electric
displacement can be obtained by integrating over the surface S. Then according to the Gauss's law
Instead of discrete charges , , ...  if there is a continious distribution of charge inside the closed
surface, we have to find total charge by integrating over the enclosed volume. The distributed charges can be
correctly represented by a charge density  which in general is a function of space. The  is the charge per
unit volume having units . The charge in a small volume dV will be . The total charge
enclosed by the volume can be obtained by integrating over the volume V. For distributed charges then
becomes
This is the Gauss law in the integral form
  
The equivalent differential form can be obtained by applying the Divergence theorem to the above eqn.
Substituting and bringing all the terms on the left hand side of the equality sign we get
This is the differential form of the Gauss's law.
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
 
Gauss's Law for Magnetic Flux Density
The total magnetic flux coming out of a closed surface is equal to the total magnetic charges (poles) inside the surface.
However there are no isolated magnetic monopoles. The magnetic poles are always found in pair with opposite polarity.
As a result, there are always equal number of north and south poles inside any closed surface making net magnetic
charges identically zero inside a volume. The total outward magnetic flux from any closed 
surface therefore must identically be equal to zero. Writing mathematically,
Where B is the magnetic flux density. Applying the Divergence theorem we get
 or
 Module 3 : Maxwell's Equations
Lecture 21 : Basic Laws of Electromagnetics
   Recap
   In this course you have learnt the following
Gauss's Law
Gauss's Law for Magnetic Flux Density
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