Detailed Notes: Dielectrics & Capacitance | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) PDF Download

 Page 1


Behavior of conductors in an electric field: 
Conductors: 
Materials in which it is easy for charges to move around. We will discuss conductors in some depth 
when we discuss currents; for now, we will just summarize a few of their properties. Among the best 
conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a 
crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of 
metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in 
place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the 
negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but 
also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of 
some external field, the electrons are free to move around. 
 
 
 
Electric fields and conductors For the rest of this lecture, we will assume that conductors are materials 
that have an infinite supply of charges that are free to move around. (This of course just an idealization; 
but, it turns out to be an extremely good one. Real conductors in fact behave very similar to this limit.) 
From this, we can deduce a few important facts about conductors and electrostatic fields 
• There is no electric field inside a conductor: Why? Suppose we bring a plus charge near a conductor. 
For a very short moment, there will be an electric field inside the conductor. However, this field will act 
on and move the electrons, which are free to move about. The electrons will move close to the plus 
charge, leaving net positive charge behind. The conductor’s charges will continue to move until the 
“external” E~ -field is cancelled out — at that point there is no longer an E~ -field to move them, so  
they stay still. 
• Net charge can only reside on the surface of a conductor:This is easily proved with Gauss’s law: 
make a little Gaussian surface that is totally contained inside the conductor. Since there is no E~ -field 
inside the conductor, H E~ · dA~ is clearly zero for your surface. Since that is equal to the charge the 
surface contains, there can be no charge. We will discuss the charge on the conductor’s surface in a 
moment. 
Page 2


Behavior of conductors in an electric field: 
Conductors: 
Materials in which it is easy for charges to move around. We will discuss conductors in some depth 
when we discuss currents; for now, we will just summarize a few of their properties. Among the best 
conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a 
crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of 
metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in 
place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the 
negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but 
also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of 
some external field, the electrons are free to move around. 
 
 
 
Electric fields and conductors For the rest of this lecture, we will assume that conductors are materials 
that have an infinite supply of charges that are free to move around. (This of course just an idealization; 
but, it turns out to be an extremely good one. Real conductors in fact behave very similar to this limit.) 
From this, we can deduce a few important facts about conductors and electrostatic fields 
• There is no electric field inside a conductor: Why? Suppose we bring a plus charge near a conductor. 
For a very short moment, there will be an electric field inside the conductor. However, this field will act 
on and move the electrons, which are free to move about. The electrons will move close to the plus 
charge, leaving net positive charge behind. The conductor’s charges will continue to move until the 
“external” E~ -field is cancelled out — at that point there is no longer an E~ -field to move them, so  
they stay still. 
• Net charge can only reside on the surface of a conductor:This is easily proved with Gauss’s law: 
make a little Gaussian surface that is totally contained inside the conductor. Since there is no E~ -field 
inside the conductor, H E~ · dA~ is clearly zero for your surface. Since that is equal to the charge the 
surface contains, there can be no charge. We will discuss the charge on the conductor’s surface in a 
moment. 
 
 
• Any external electric field lines are perpendicular to the surface: Another way to put this is that 
there is no component of electric field that is tangent to the surface. We prove this by contradiction: 
suppose that a component of the E~ -field were tangent to the surface. If that were the case, then charges 
would flow along the surface. They would continue to flow until there was no longer any tangential 
component to the E~ -field. Hence, this situation cannot exist: even if it exists momentarily, it will 
rapidly (within 10-17 seconds or so) correct itself. 
• The conductor’s surface is an equipotential: This follows from the fact that the E~ -field is 
perpendicular to the surface. We do a line integral of E~ on the surface; the path is perpendicular to the 
field; so the difference in potential between any two points on the surface is zero. 
 
Insulators: 
 
Insulators, on the other hand, are substances that have exactly the opposite effect on the flow of 
electrons. These substances impede the free flow of electrons, thereby inhibiting the flow of electrical 
current. Insulators contain atoms that hold on to their electrons tightly which restrict the flow of 
electrons from one atom to another. Because of the tightly bound electrons, they are not able to roam 
around freely. In simple terms, substances that prevent the flow of current are insulators. The materials 
have such low conductivity that the flow of current is almost negligible, thus they are commonly used to 
protect us from dangerous effects of electricity. 
Some common examples of insulators are glass, plastic, ceramics, paper, rubber, etc. The flow of 
current in electronic circuits is not static and voltage can be quite high at times, which makes it a little 
vulnerable. Sometimes the voltage is high enough to cause electric current to flow through materials that 
are not even considered as good conductors of electricity. This can cause electric shock because human 
body is also a good conductor of electricity. Therefore, electric wires are coated with rubber which acts 
as an insulator which in turn protects us from the conductor inside. 
Page 3


Behavior of conductors in an electric field: 
Conductors: 
Materials in which it is easy for charges to move around. We will discuss conductors in some depth 
when we discuss currents; for now, we will just summarize a few of their properties. Among the best 
conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a 
crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of 
metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in 
place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the 
negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but 
also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of 
some external field, the electrons are free to move around. 
 
 
 
Electric fields and conductors For the rest of this lecture, we will assume that conductors are materials 
that have an infinite supply of charges that are free to move around. (This of course just an idealization; 
but, it turns out to be an extremely good one. Real conductors in fact behave very similar to this limit.) 
From this, we can deduce a few important facts about conductors and electrostatic fields 
• There is no electric field inside a conductor: Why? Suppose we bring a plus charge near a conductor. 
For a very short moment, there will be an electric field inside the conductor. However, this field will act 
on and move the electrons, which are free to move about. The electrons will move close to the plus 
charge, leaving net positive charge behind. The conductor’s charges will continue to move until the 
“external” E~ -field is cancelled out — at that point there is no longer an E~ -field to move them, so  
they stay still. 
• Net charge can only reside on the surface of a conductor:This is easily proved with Gauss’s law: 
make a little Gaussian surface that is totally contained inside the conductor. Since there is no E~ -field 
inside the conductor, H E~ · dA~ is clearly zero for your surface. Since that is equal to the charge the 
surface contains, there can be no charge. We will discuss the charge on the conductor’s surface in a 
moment. 
 
 
• Any external electric field lines are perpendicular to the surface: Another way to put this is that 
there is no component of electric field that is tangent to the surface. We prove this by contradiction: 
suppose that a component of the E~ -field were tangent to the surface. If that were the case, then charges 
would flow along the surface. They would continue to flow until there was no longer any tangential 
component to the E~ -field. Hence, this situation cannot exist: even if it exists momentarily, it will 
rapidly (within 10-17 seconds or so) correct itself. 
• The conductor’s surface is an equipotential: This follows from the fact that the E~ -field is 
perpendicular to the surface. We do a line integral of E~ on the surface; the path is perpendicular to the 
field; so the difference in potential between any two points on the surface is zero. 
 
Insulators: 
 
Insulators, on the other hand, are substances that have exactly the opposite effect on the flow of 
electrons. These substances impede the free flow of electrons, thereby inhibiting the flow of electrical 
current. Insulators contain atoms that hold on to their electrons tightly which restrict the flow of 
electrons from one atom to another. Because of the tightly bound electrons, they are not able to roam 
around freely. In simple terms, substances that prevent the flow of current are insulators. The materials 
have such low conductivity that the flow of current is almost negligible, thus they are commonly used to 
protect us from dangerous effects of electricity. 
Some common examples of insulators are glass, plastic, ceramics, paper, rubber, etc. The flow of 
current in electronic circuits is not static and voltage can be quite high at times, which makes it a little 
vulnerable. Sometimes the voltage is high enough to cause electric current to flow through materials that 
are not even considered as good conductors of electricity. This can cause electric shock because human 
body is also a good conductor of electricity. Therefore, electric wires are coated with rubber which acts 
as an insulator which in turn protects us from the conductor inside. 
Conductors vs. Insulators: Comparison Chart 
 
 
 
 
 
Page 4


Behavior of conductors in an electric field: 
Conductors: 
Materials in which it is easy for charges to move around. We will discuss conductors in some depth 
when we discuss currents; for now, we will just summarize a few of their properties. Among the best 
conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a 
crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of 
metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in 
place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the 
negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but 
also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of 
some external field, the electrons are free to move around. 
 
 
 
Electric fields and conductors For the rest of this lecture, we will assume that conductors are materials 
that have an infinite supply of charges that are free to move around. (This of course just an idealization; 
but, it turns out to be an extremely good one. Real conductors in fact behave very similar to this limit.) 
From this, we can deduce a few important facts about conductors and electrostatic fields 
• There is no electric field inside a conductor: Why? Suppose we bring a plus charge near a conductor. 
For a very short moment, there will be an electric field inside the conductor. However, this field will act 
on and move the electrons, which are free to move about. The electrons will move close to the plus 
charge, leaving net positive charge behind. The conductor’s charges will continue to move until the 
“external” E~ -field is cancelled out — at that point there is no longer an E~ -field to move them, so  
they stay still. 
• Net charge can only reside on the surface of a conductor:This is easily proved with Gauss’s law: 
make a little Gaussian surface that is totally contained inside the conductor. Since there is no E~ -field 
inside the conductor, H E~ · dA~ is clearly zero for your surface. Since that is equal to the charge the 
surface contains, there can be no charge. We will discuss the charge on the conductor’s surface in a 
moment. 
 
 
• Any external electric field lines are perpendicular to the surface: Another way to put this is that 
there is no component of electric field that is tangent to the surface. We prove this by contradiction: 
suppose that a component of the E~ -field were tangent to the surface. If that were the case, then charges 
would flow along the surface. They would continue to flow until there was no longer any tangential 
component to the E~ -field. Hence, this situation cannot exist: even if it exists momentarily, it will 
rapidly (within 10-17 seconds or so) correct itself. 
• The conductor’s surface is an equipotential: This follows from the fact that the E~ -field is 
perpendicular to the surface. We do a line integral of E~ on the surface; the path is perpendicular to the 
field; so the difference in potential between any two points on the surface is zero. 
 
Insulators: 
 
Insulators, on the other hand, are substances that have exactly the opposite effect on the flow of 
electrons. These substances impede the free flow of electrons, thereby inhibiting the flow of electrical 
current. Insulators contain atoms that hold on to their electrons tightly which restrict the flow of 
electrons from one atom to another. Because of the tightly bound electrons, they are not able to roam 
around freely. In simple terms, substances that prevent the flow of current are insulators. The materials 
have such low conductivity that the flow of current is almost negligible, thus they are commonly used to 
protect us from dangerous effects of electricity. 
Some common examples of insulators are glass, plastic, ceramics, paper, rubber, etc. The flow of 
current in electronic circuits is not static and voltage can be quite high at times, which makes it a little 
vulnerable. Sometimes the voltage is high enough to cause electric current to flow through materials that 
are not even considered as good conductors of electricity. This can cause electric shock because human 
body is also a good conductor of electricity. Therefore, electric wires are coated with rubber which acts 
as an insulator which in turn protects us from the conductor inside. 
Conductors vs. Insulators: Comparison Chart 
 
 
 
 
 
Electric field inside a dielectric material – polarization: 
 
Page 5


Behavior of conductors in an electric field: 
Conductors: 
Materials in which it is easy for charges to move around. We will discuss conductors in some depth 
when we discuss currents; for now, we will just summarize a few of their properties. Among the best 
conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a 
crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of 
metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in 
place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the 
negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but 
also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of 
some external field, the electrons are free to move around. 
 
 
 
Electric fields and conductors For the rest of this lecture, we will assume that conductors are materials 
that have an infinite supply of charges that are free to move around. (This of course just an idealization; 
but, it turns out to be an extremely good one. Real conductors in fact behave very similar to this limit.) 
From this, we can deduce a few important facts about conductors and electrostatic fields 
• There is no electric field inside a conductor: Why? Suppose we bring a plus charge near a conductor. 
For a very short moment, there will be an electric field inside the conductor. However, this field will act 
on and move the electrons, which are free to move about. The electrons will move close to the plus 
charge, leaving net positive charge behind. The conductor’s charges will continue to move until the 
“external” E~ -field is cancelled out — at that point there is no longer an E~ -field to move them, so  
they stay still. 
• Net charge can only reside on the surface of a conductor:This is easily proved with Gauss’s law: 
make a little Gaussian surface that is totally contained inside the conductor. Since there is no E~ -field 
inside the conductor, H E~ · dA~ is clearly zero for your surface. Since that is equal to the charge the 
surface contains, there can be no charge. We will discuss the charge on the conductor’s surface in a 
moment. 
 
 
• Any external electric field lines are perpendicular to the surface: Another way to put this is that 
there is no component of electric field that is tangent to the surface. We prove this by contradiction: 
suppose that a component of the E~ -field were tangent to the surface. If that were the case, then charges 
would flow along the surface. They would continue to flow until there was no longer any tangential 
component to the E~ -field. Hence, this situation cannot exist: even if it exists momentarily, it will 
rapidly (within 10-17 seconds or so) correct itself. 
• The conductor’s surface is an equipotential: This follows from the fact that the E~ -field is 
perpendicular to the surface. We do a line integral of E~ on the surface; the path is perpendicular to the 
field; so the difference in potential between any two points on the surface is zero. 
 
Insulators: 
 
Insulators, on the other hand, are substances that have exactly the opposite effect on the flow of 
electrons. These substances impede the free flow of electrons, thereby inhibiting the flow of electrical 
current. Insulators contain atoms that hold on to their electrons tightly which restrict the flow of 
electrons from one atom to another. Because of the tightly bound electrons, they are not able to roam 
around freely. In simple terms, substances that prevent the flow of current are insulators. The materials 
have such low conductivity that the flow of current is almost negligible, thus they are commonly used to 
protect us from dangerous effects of electricity. 
Some common examples of insulators are glass, plastic, ceramics, paper, rubber, etc. The flow of 
current in electronic circuits is not static and voltage can be quite high at times, which makes it a little 
vulnerable. Sometimes the voltage is high enough to cause electric current to flow through materials that 
are not even considered as good conductors of electricity. This can cause electric shock because human 
body is also a good conductor of electricity. Therefore, electric wires are coated with rubber which acts 
as an insulator which in turn protects us from the conductor inside. 
Conductors vs. Insulators: Comparison Chart 
 
 
 
 
 
Electric field inside a dielectric material – polarization: