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1 | 6190-6193 | If we generalise
this law by adding to the total current carried by conductors through
the surface, another term which is e0 times the rate of change of electric
flux through the same surface, the total has the same value of current i
for all surfaces If this is done, there is no contradiction in the value of B
obtained anywhere using the generalised Ampere’s law B at the point P
is non-zero no matter which surface is used for calculating it B at a
point P outside the plates [Fig |
1 | 6191-6194 | If this is done, there is no contradiction in the value of B
obtained anywhere using the generalised Ampere’s law B at the point P
is non-zero no matter which surface is used for calculating it B at a
point P outside the plates [Fig 8 |
1 | 6192-6195 | B at the point P
is non-zero no matter which surface is used for calculating it B at a
point P outside the plates [Fig 8 1(a)] is the same as at a point M just
inside, as it should be |
1 | 6193-6196 | B at a
point P outside the plates [Fig 8 1(a)] is the same as at a point M just
inside, as it should be The current carried by conductors due to flow of
charges is called conduction current |
1 | 6194-6197 | 8 1(a)] is the same as at a point M just
inside, as it should be The current carried by conductors due to flow of
charges is called conduction current The current, given by Eq |
1 | 6195-6198 | 1(a)] is the same as at a point M just
inside, as it should be The current carried by conductors due to flow of
charges is called conduction current The current, given by Eq (8 |
1 | 6196-6199 | The current carried by conductors due to flow of
charges is called conduction current The current, given by Eq (8 4), is a
new term, and is due to changing electric field (or electric displacement,
an old term still used sometimes) |
1 | 6197-6200 | The current, given by Eq (8 4), is a
new term, and is due to changing electric field (or electric displacement,
an old term still used sometimes) It is, therefore, called displacement
current or Maxwell’s displacement current |
1 | 6198-6201 | (8 4), is a
new term, and is due to changing electric field (or electric displacement,
an old term still used sometimes) It is, therefore, called displacement
current or Maxwell’s displacement current Figure 8 |
1 | 6199-6202 | 4), is a
new term, and is due to changing electric field (or electric displacement,
an old term still used sometimes) It is, therefore, called displacement
current or Maxwell’s displacement current Figure 8 2 shows the electric
and magnetic fields inside the parallel plate capacitor discussed above |
1 | 6200-6203 | It is, therefore, called displacement
current or Maxwell’s displacement current Figure 8 2 shows the electric
and magnetic fields inside the parallel plate capacitor discussed above The generalisation made by Maxwell then is the following |
1 | 6201-6204 | Figure 8 2 shows the electric
and magnetic fields inside the parallel plate capacitor discussed above The generalisation made by Maxwell then is the following The source
of a magnetic field is not just the conduction electric current due to flowing
FIGURE 8 |
1 | 6202-6205 | 2 shows the electric
and magnetic fields inside the parallel plate capacitor discussed above The generalisation made by Maxwell then is the following The source
of a magnetic field is not just the conduction electric current due to flowing
FIGURE 8 1 A
parallel plate
capacitor C, as part of
a circuit through
which a time
dependent current
i (t) flows, (a) a loop of
radius r, to determine
magnetic field at a
point P on the loop;
(b) a pot-shaped
surface passing
through the interior
between the capacitor
plates with the loop
shown in (a) as its
rim; (c) a tiffin-
shaped surface with
the circular loop as
its rim and a flat
circular bottom S
between the capacitor
plates |
1 | 6203-6206 | The generalisation made by Maxwell then is the following The source
of a magnetic field is not just the conduction electric current due to flowing
FIGURE 8 1 A
parallel plate
capacitor C, as part of
a circuit through
which a time
dependent current
i (t) flows, (a) a loop of
radius r, to determine
magnetic field at a
point P on the loop;
(b) a pot-shaped
surface passing
through the interior
between the capacitor
plates with the loop
shown in (a) as its
rim; (c) a tiffin-
shaped surface with
the circular loop as
its rim and a flat
circular bottom S
between the capacitor
plates The arrows
show uniform electric
field between the
capacitor plates |
1 | 6204-6207 | The source
of a magnetic field is not just the conduction electric current due to flowing
FIGURE 8 1 A
parallel plate
capacitor C, as part of
a circuit through
which a time
dependent current
i (t) flows, (a) a loop of
radius r, to determine
magnetic field at a
point P on the loop;
(b) a pot-shaped
surface passing
through the interior
between the capacitor
plates with the loop
shown in (a) as its
rim; (c) a tiffin-
shaped surface with
the circular loop as
its rim and a flat
circular bottom S
between the capacitor
plates The arrows
show uniform electric
field between the
capacitor plates Rationalised 2023-24
Physics
204
charges, but also the time rate of change of electric field |
1 | 6205-6208 | 1 A
parallel plate
capacitor C, as part of
a circuit through
which a time
dependent current
i (t) flows, (a) a loop of
radius r, to determine
magnetic field at a
point P on the loop;
(b) a pot-shaped
surface passing
through the interior
between the capacitor
plates with the loop
shown in (a) as its
rim; (c) a tiffin-
shaped surface with
the circular loop as
its rim and a flat
circular bottom S
between the capacitor
plates The arrows
show uniform electric
field between the
capacitor plates Rationalised 2023-24
Physics
204
charges, but also the time rate of change of electric field More
precisely, the total current i is the sum of the conduction current
denoted by ic, and the displacement current denoted by id (= e0 (dFE/
dt)) |
1 | 6206-6209 | The arrows
show uniform electric
field between the
capacitor plates Rationalised 2023-24
Physics
204
charges, but also the time rate of change of electric field More
precisely, the total current i is the sum of the conduction current
denoted by ic, and the displacement current denoted by id (= e0 (dFE/
dt)) So we have
0
d
d
E
c
d
c
i
i
i
i
Φt
ε
=
+
=
+
(8 |
1 | 6207-6210 | Rationalised 2023-24
Physics
204
charges, but also the time rate of change of electric field More
precisely, the total current i is the sum of the conduction current
denoted by ic, and the displacement current denoted by id (= e0 (dFE/
dt)) So we have
0
d
d
E
c
d
c
i
i
i
i
Φt
ε
=
+
=
+
(8 5)
In explicit terms, this means that outside the capacitor plates,
we have only conduction current ic = i, and no displacement
current, i |
1 | 6208-6211 | More
precisely, the total current i is the sum of the conduction current
denoted by ic, and the displacement current denoted by id (= e0 (dFE/
dt)) So we have
0
d
d
E
c
d
c
i
i
i
i
Φt
ε
=
+
=
+
(8 5)
In explicit terms, this means that outside the capacitor plates,
we have only conduction current ic = i, and no displacement
current, i e |
1 | 6209-6212 | So we have
0
d
d
E
c
d
c
i
i
i
i
Φt
ε
=
+
=
+
(8 5)
In explicit terms, this means that outside the capacitor plates,
we have only conduction current ic = i, and no displacement
current, i e , id = 0 |
1 | 6210-6213 | 5)
In explicit terms, this means that outside the capacitor plates,
we have only conduction current ic = i, and no displacement
current, i e , id = 0 On the other hand, inside the capacitor, there is
no conduction current, i |
1 | 6211-6214 | e , id = 0 On the other hand, inside the capacitor, there is
no conduction current, i e |
1 | 6212-6215 | , id = 0 On the other hand, inside the capacitor, there is
no conduction current, i e , ic = 0, and there is only displacement
current, so that id = i |
1 | 6213-6216 | On the other hand, inside the capacitor, there is
no conduction current, i e , ic = 0, and there is only displacement
current, so that id = i The generalised (and correct) Ampere’s circuital law has the same
form as Eq |
1 | 6214-6217 | e , ic = 0, and there is only displacement
current, so that id = i The generalised (and correct) Ampere’s circuital law has the same
form as Eq (8 |
1 | 6215-6218 | , ic = 0, and there is only displacement
current, so that id = i The generalised (and correct) Ampere’s circuital law has the same
form as Eq (8 1), with one difference: “the total current passing
through any surface of which the closed loop is the perimeter” is
the sum of the conduction current and the displacement current |
1 | 6216-6219 | The generalised (and correct) Ampere’s circuital law has the same
form as Eq (8 1), with one difference: “the total current passing
through any surface of which the closed loop is the perimeter” is
the sum of the conduction current and the displacement current The generalised law is
B
�gl
d =
d
d
0
µ
µ
ε
0
0
i
t
c
E
+
∫
Φ
(8 |
1 | 6217-6220 | (8 1), with one difference: “the total current passing
through any surface of which the closed loop is the perimeter” is
the sum of the conduction current and the displacement current The generalised law is
B
�gl
d =
d
d
0
µ
µ
ε
0
0
i
t
c
E
+
∫
Φ
(8 6)
and is known as Ampere-Maxwell law |
1 | 6218-6221 | 1), with one difference: “the total current passing
through any surface of which the closed loop is the perimeter” is
the sum of the conduction current and the displacement current The generalised law is
B
�gl
d =
d
d
0
µ
µ
ε
0
0
i
t
c
E
+
∫
Φ
(8 6)
and is known as Ampere-Maxwell law In all respects, the displacement current has the same physical
effects as the conduction current |
1 | 6219-6222 | The generalised law is
B
�gl
d =
d
d
0
µ
µ
ε
0
0
i
t
c
E
+
∫
Φ
(8 6)
and is known as Ampere-Maxwell law In all respects, the displacement current has the same physical
effects as the conduction current In some cases, for example, steady
electric fields in a conducting wire, the displacement current may
be zero since the electric field E does not change with time |
1 | 6220-6223 | 6)
and is known as Ampere-Maxwell law In all respects, the displacement current has the same physical
effects as the conduction current In some cases, for example, steady
electric fields in a conducting wire, the displacement current may
be zero since the electric field E does not change with time In other
cases, for example, the charging capacitor above, both conduction
and displacement currents may be present in different regions of
space |
1 | 6221-6224 | In all respects, the displacement current has the same physical
effects as the conduction current In some cases, for example, steady
electric fields in a conducting wire, the displacement current may
be zero since the electric field E does not change with time In other
cases, for example, the charging capacitor above, both conduction
and displacement currents may be present in different regions of
space In most of the cases, they both may be present in the same
region of space, as there exist no perfectly conducting or perfectly
insulating medium |
1 | 6222-6225 | In some cases, for example, steady
electric fields in a conducting wire, the displacement current may
be zero since the electric field E does not change with time In other
cases, for example, the charging capacitor above, both conduction
and displacement currents may be present in different regions of
space In most of the cases, they both may be present in the same
region of space, as there exist no perfectly conducting or perfectly
insulating medium Most interestingly, there may be large regions
of space where there is no conduction current, but there is only a
displacement current due to time-varying electric fields |
1 | 6223-6226 | In other
cases, for example, the charging capacitor above, both conduction
and displacement currents may be present in different regions of
space In most of the cases, they both may be present in the same
region of space, as there exist no perfectly conducting or perfectly
insulating medium Most interestingly, there may be large regions
of space where there is no conduction current, but there is only a
displacement current due to time-varying electric fields In such a
region, we expect a magnetic field, though there is no (conduction)
current source nearby |
1 | 6224-6227 | In most of the cases, they both may be present in the same
region of space, as there exist no perfectly conducting or perfectly
insulating medium Most interestingly, there may be large regions
of space where there is no conduction current, but there is only a
displacement current due to time-varying electric fields In such a
region, we expect a magnetic field, though there is no (conduction)
current source nearby The prediction of such a displacement current
can be verified experimentally |
1 | 6225-6228 | Most interestingly, there may be large regions
of space where there is no conduction current, but there is only a
displacement current due to time-varying electric fields In such a
region, we expect a magnetic field, though there is no (conduction)
current source nearby The prediction of such a displacement current
can be verified experimentally For example, a magnetic field (say at point
M) between the plates of the capacitor in Fig |
1 | 6226-6229 | In such a
region, we expect a magnetic field, though there is no (conduction)
current source nearby The prediction of such a displacement current
can be verified experimentally For example, a magnetic field (say at point
M) between the plates of the capacitor in Fig 8 |
1 | 6227-6230 | The prediction of such a displacement current
can be verified experimentally For example, a magnetic field (say at point
M) between the plates of the capacitor in Fig 8 2(a) can be measured and
is seen to be the same as that just outside (at P) |
1 | 6228-6231 | For example, a magnetic field (say at point
M) between the plates of the capacitor in Fig 8 2(a) can be measured and
is seen to be the same as that just outside (at P) The displacement current has (literally) far reaching consequences |
1 | 6229-6232 | 8 2(a) can be measured and
is seen to be the same as that just outside (at P) The displacement current has (literally) far reaching consequences One thing we immediately notice is that the laws of electricity and
magnetism are now more symmetrical* |
1 | 6230-6233 | 2(a) can be measured and
is seen to be the same as that just outside (at P) The displacement current has (literally) far reaching consequences One thing we immediately notice is that the laws of electricity and
magnetism are now more symmetrical* Faraday’s law of induction states
that there is an induced emf equal to the rate of change of magnetic flux |
1 | 6231-6234 | The displacement current has (literally) far reaching consequences One thing we immediately notice is that the laws of electricity and
magnetism are now more symmetrical* Faraday’s law of induction states
that there is an induced emf equal to the rate of change of magnetic flux Now, since the emf between two points 1 and 2 is the work done per unit
charge in taking it from 1 to 2, the existence of an emf implies the existence
of an electric field |
1 | 6232-6235 | One thing we immediately notice is that the laws of electricity and
magnetism are now more symmetrical* Faraday’s law of induction states
that there is an induced emf equal to the rate of change of magnetic flux Now, since the emf between two points 1 and 2 is the work done per unit
charge in taking it from 1 to 2, the existence of an emf implies the existence
of an electric field So, we can rephrase Faraday’s law of electromagnetic
induction by saying that a magnetic field, changing with time, gives rise
to an electric field |
1 | 6233-6236 | Faraday’s law of induction states
that there is an induced emf equal to the rate of change of magnetic flux Now, since the emf between two points 1 and 2 is the work done per unit
charge in taking it from 1 to 2, the existence of an emf implies the existence
of an electric field So, we can rephrase Faraday’s law of electromagnetic
induction by saying that a magnetic field, changing with time, gives rise
to an electric field Then, the fact that an electric field changing with
time gives rise to a magnetic field, is the symmetrical counterpart, and is
FIGURE 8 |
1 | 6234-6237 | Now, since the emf between two points 1 and 2 is the work done per unit
charge in taking it from 1 to 2, the existence of an emf implies the existence
of an electric field So, we can rephrase Faraday’s law of electromagnetic
induction by saying that a magnetic field, changing with time, gives rise
to an electric field Then, the fact that an electric field changing with
time gives rise to a magnetic field, is the symmetrical counterpart, and is
FIGURE 8 2 (a) The
electric and magnetic
fields E and B between
the capacitor plates, at
the point M |
1 | 6235-6238 | So, we can rephrase Faraday’s law of electromagnetic
induction by saying that a magnetic field, changing with time, gives rise
to an electric field Then, the fact that an electric field changing with
time gives rise to a magnetic field, is the symmetrical counterpart, and is
FIGURE 8 2 (a) The
electric and magnetic
fields E and B between
the capacitor plates, at
the point M (b) A cross
sectional view of Fig |
1 | 6236-6239 | Then, the fact that an electric field changing with
time gives rise to a magnetic field, is the symmetrical counterpart, and is
FIGURE 8 2 (a) The
electric and magnetic
fields E and B between
the capacitor plates, at
the point M (b) A cross
sectional view of Fig (a) |
1 | 6237-6240 | 2 (a) The
electric and magnetic
fields E and B between
the capacitor plates, at
the point M (b) A cross
sectional view of Fig (a) *
They are still not perfectly symmetrical; there are no known sources of magnetic
field (magnetic monopoles) analogous to electric charges which are sources of
electric field |
1 | 6238-6241 | (b) A cross
sectional view of Fig (a) *
They are still not perfectly symmetrical; there are no known sources of magnetic
field (magnetic monopoles) analogous to electric charges which are sources of
electric field Rationalised 2023-24
205
Electromagnetic
Waves
a consequence of the displacement current being a source of a magnetic
field |
1 | 6239-6242 | (a) *
They are still not perfectly symmetrical; there are no known sources of magnetic
field (magnetic monopoles) analogous to electric charges which are sources of
electric field Rationalised 2023-24
205
Electromagnetic
Waves
a consequence of the displacement current being a source of a magnetic
field Thus, time- dependent electric and magnetic fields give rise to each
other |
1 | 6240-6243 | *
They are still not perfectly symmetrical; there are no known sources of magnetic
field (magnetic monopoles) analogous to electric charges which are sources of
electric field Rationalised 2023-24
205
Electromagnetic
Waves
a consequence of the displacement current being a source of a magnetic
field Thus, time- dependent electric and magnetic fields give rise to each
other Faraday’s law of electromagnetic induction and Ampere-Maxwell
law give a quantitative expression of this statement, with the current
being the total current, as in Eq |
1 | 6241-6244 | Rationalised 2023-24
205
Electromagnetic
Waves
a consequence of the displacement current being a source of a magnetic
field Thus, time- dependent electric and magnetic fields give rise to each
other Faraday’s law of electromagnetic induction and Ampere-Maxwell
law give a quantitative expression of this statement, with the current
being the total current, as in Eq (8 |
1 | 6242-6245 | Thus, time- dependent electric and magnetic fields give rise to each
other Faraday’s law of electromagnetic induction and Ampere-Maxwell
law give a quantitative expression of this statement, with the current
being the total current, as in Eq (8 5) |
1 | 6243-6246 | Faraday’s law of electromagnetic induction and Ampere-Maxwell
law give a quantitative expression of this statement, with the current
being the total current, as in Eq (8 5) One very important consequence
of this symmetry is the existence of electromagnetic waves, which we
discuss qualitatively in the next section |
1 | 6244-6247 | (8 5) One very important consequence
of this symmetry is the existence of electromagnetic waves, which we
discuss qualitatively in the next section MAXWELL’S EQUATIONS IN VACUUM
1 |
1 | 6245-6248 | 5) One very important consequence
of this symmetry is the existence of electromagnetic waves, which we
discuss qualitatively in the next section MAXWELL’S EQUATIONS IN VACUUM
1 “E |
1 | 6246-6249 | One very important consequence
of this symmetry is the existence of electromagnetic waves, which we
discuss qualitatively in the next section MAXWELL’S EQUATIONS IN VACUUM
1 “E dA = Q/✒0
(Gauss’s Law for electricity)
2 |
1 | 6247-6250 | MAXWELL’S EQUATIONS IN VACUUM
1 “E dA = Q/✒0
(Gauss’s Law for electricity)
2 “B |
1 | 6248-6251 | “E dA = Q/✒0
(Gauss’s Law for electricity)
2 “B dA = 0
(Gauss’s Law for magnetism)
3 |
1 | 6249-6252 | dA = Q/✒0
(Gauss’s Law for electricity)
2 “B dA = 0
(Gauss’s Law for magnetism)
3 “E |
1 | 6250-6253 | “B dA = 0
(Gauss’s Law for magnetism)
3 “E dl = –d
d
tΦB
l=
(Faraday’s Law)
4 |
1 | 6251-6254 | dA = 0
(Gauss’s Law for magnetism)
3 “E dl = –d
d
tΦB
l=
(Faraday’s Law)
4 “B |
1 | 6252-6255 | “E dl = –d
d
tΦB
l=
(Faraday’s Law)
4 “B dl ==
d
d
0
µ
µ ε
0
0
i
t
c
E
+
Φ
(Ampere – Maxwell Law)
8 |
1 | 6253-6256 | dl = –d
d
tΦB
l=
(Faraday’s Law)
4 “B dl ==
d
d
0
µ
µ ε
0
0
i
t
c
E
+
Φ
(Ampere – Maxwell Law)
8 3 ELECTROMAGNETIC WAVES
8 |
1 | 6254-6257 | “B dl ==
d
d
0
µ
µ ε
0
0
i
t
c
E
+
Φ
(Ampere – Maxwell Law)
8 3 ELECTROMAGNETIC WAVES
8 3 |
1 | 6255-6258 | dl ==
d
d
0
µ
µ ε
0
0
i
t
c
E
+
Φ
(Ampere – Maxwell Law)
8 3 ELECTROMAGNETIC WAVES
8 3 1 Sources of electromagnetic waves
How are electromagnetic waves produced |
1 | 6256-6259 | 3 ELECTROMAGNETIC WAVES
8 3 1 Sources of electromagnetic waves
How are electromagnetic waves produced Neither stationary charges
nor charges in uniform motion (steady currents) can be sources of
electromagnetic waves |
1 | 6257-6260 | 3 1 Sources of electromagnetic waves
How are electromagnetic waves produced Neither stationary charges
nor charges in uniform motion (steady currents) can be sources of
electromagnetic waves The former produces only electrostatic fields, while
the latter produces magnetic fields that, however, do not vary with time |
1 | 6258-6261 | 1 Sources of electromagnetic waves
How are electromagnetic waves produced Neither stationary charges
nor charges in uniform motion (steady currents) can be sources of
electromagnetic waves The former produces only electrostatic fields, while
the latter produces magnetic fields that, however, do not vary with time It is an important result of Maxwell’s theory that accelerated charges
radiate electromagnetic waves |
1 | 6259-6262 | Neither stationary charges
nor charges in uniform motion (steady currents) can be sources of
electromagnetic waves The former produces only electrostatic fields, while
the latter produces magnetic fields that, however, do not vary with time It is an important result of Maxwell’s theory that accelerated charges
radiate electromagnetic waves The proof of this basic result is beyond
the scope of this book, but we can accept it on the basis of rough,
qualitative reasoning |
1 | 6260-6263 | The former produces only electrostatic fields, while
the latter produces magnetic fields that, however, do not vary with time It is an important result of Maxwell’s theory that accelerated charges
radiate electromagnetic waves The proof of this basic result is beyond
the scope of this book, but we can accept it on the basis of rough,
qualitative reasoning Consider a charge oscillating with some frequency |
1 | 6261-6264 | It is an important result of Maxwell’s theory that accelerated charges
radiate electromagnetic waves The proof of this basic result is beyond
the scope of this book, but we can accept it on the basis of rough,
qualitative reasoning Consider a charge oscillating with some frequency (An oscillating charge is an example of accelerating charge |
1 | 6262-6265 | The proof of this basic result is beyond
the scope of this book, but we can accept it on the basis of rough,
qualitative reasoning Consider a charge oscillating with some frequency (An oscillating charge is an example of accelerating charge ) This
produces an oscillating electric field in space, which produces an
oscillating magnetic field, which in turn, is a source of oscillating electric
field, and so on |
1 | 6263-6266 | Consider a charge oscillating with some frequency (An oscillating charge is an example of accelerating charge ) This
produces an oscillating electric field in space, which produces an
oscillating magnetic field, which in turn, is a source of oscillating electric
field, and so on The oscillating electric and magnetic fields thus
regenerate each other, so to speak, as the wave propagates through the
space |
1 | 6264-6267 | (An oscillating charge is an example of accelerating charge ) This
produces an oscillating electric field in space, which produces an
oscillating magnetic field, which in turn, is a source of oscillating electric
field, and so on The oscillating electric and magnetic fields thus
regenerate each other, so to speak, as the wave propagates through the
space The frequency of the electromagnetic wave naturally equals the
frequency of oscillation of the charge |
1 | 6265-6268 | ) This
produces an oscillating electric field in space, which produces an
oscillating magnetic field, which in turn, is a source of oscillating electric
field, and so on The oscillating electric and magnetic fields thus
regenerate each other, so to speak, as the wave propagates through the
space The frequency of the electromagnetic wave naturally equals the
frequency of oscillation of the charge The energy associated with the
propagating wave comes at the expense of the energy of the source – the
accelerated charge |
1 | 6266-6269 | The oscillating electric and magnetic fields thus
regenerate each other, so to speak, as the wave propagates through the
space The frequency of the electromagnetic wave naturally equals the
frequency of oscillation of the charge The energy associated with the
propagating wave comes at the expense of the energy of the source – the
accelerated charge From the preceding discussion, it might appear easy to test the
prediction that light is an electromagnetic wave |
1 | 6267-6270 | The frequency of the electromagnetic wave naturally equals the
frequency of oscillation of the charge The energy associated with the
propagating wave comes at the expense of the energy of the source – the
accelerated charge From the preceding discussion, it might appear easy to test the
prediction that light is an electromagnetic wave We might think that all
we needed to do was to set up an ac circuit in which the current oscillate
at the frequency of visible light, say, yellow light |
1 | 6268-6271 | The energy associated with the
propagating wave comes at the expense of the energy of the source – the
accelerated charge From the preceding discussion, it might appear easy to test the
prediction that light is an electromagnetic wave We might think that all
we needed to do was to set up an ac circuit in which the current oscillate
at the frequency of visible light, say, yellow light But, alas, that is not
possible |
1 | 6269-6272 | From the preceding discussion, it might appear easy to test the
prediction that light is an electromagnetic wave We might think that all
we needed to do was to set up an ac circuit in which the current oscillate
at the frequency of visible light, say, yellow light But, alas, that is not
possible The frequency of yellow light is about 6 × 1014 Hz, while the
frequency that we get even with modern electronic circuits is hardly about
1011 Hz |
1 | 6270-6273 | We might think that all
we needed to do was to set up an ac circuit in which the current oscillate
at the frequency of visible light, say, yellow light But, alas, that is not
possible The frequency of yellow light is about 6 × 1014 Hz, while the
frequency that we get even with modern electronic circuits is hardly about
1011 Hz This is why the experimental demonstration of electromagnetic
Rationalised 2023-24
Physics
206
wave had to come in the low frequency region (the radio
wave region), as in the Hertz’s experiment (1887) |
1 | 6271-6274 | But, alas, that is not
possible The frequency of yellow light is about 6 × 1014 Hz, while the
frequency that we get even with modern electronic circuits is hardly about
1011 Hz This is why the experimental demonstration of electromagnetic
Rationalised 2023-24
Physics
206
wave had to come in the low frequency region (the radio
wave region), as in the Hertz’s experiment (1887) Hertz’s successful experimental test of Maxwell’s
theory created a sensation and sparked off other
important works in this field |
1 | 6272-6275 | The frequency of yellow light is about 6 × 1014 Hz, while the
frequency that we get even with modern electronic circuits is hardly about
1011 Hz This is why the experimental demonstration of electromagnetic
Rationalised 2023-24
Physics
206
wave had to come in the low frequency region (the radio
wave region), as in the Hertz’s experiment (1887) Hertz’s successful experimental test of Maxwell’s
theory created a sensation and sparked off other
important works in this field Two important
achievements in this connection deserve mention |
1 | 6273-6276 | This is why the experimental demonstration of electromagnetic
Rationalised 2023-24
Physics
206
wave had to come in the low frequency region (the radio
wave region), as in the Hertz’s experiment (1887) Hertz’s successful experimental test of Maxwell’s
theory created a sensation and sparked off other
important works in this field Two important
achievements in this connection deserve mention Seven
years after Hertz, Jagdish Chandra Bose, working at
Calcutta (now Kolkata), succeeded in producing and
observing electromagnetic waves of much shorter
wavelength (25 mm to 5 mm) |
1 | 6274-6277 | Hertz’s successful experimental test of Maxwell’s
theory created a sensation and sparked off other
important works in this field Two important
achievements in this connection deserve mention Seven
years after Hertz, Jagdish Chandra Bose, working at
Calcutta (now Kolkata), succeeded in producing and
observing electromagnetic waves of much shorter
wavelength (25 mm to 5 mm) His experiment, like that
of Hertz’s, was confined to the laboratory |
1 | 6275-6278 | Two important
achievements in this connection deserve mention Seven
years after Hertz, Jagdish Chandra Bose, working at
Calcutta (now Kolkata), succeeded in producing and
observing electromagnetic waves of much shorter
wavelength (25 mm to 5 mm) His experiment, like that
of Hertz’s, was confined to the laboratory At around the same time, Guglielmo Marconi in Italy
followed Hertz’s work and succeeded in transmitting
electromagnetic waves over distances of many kilometres |
1 | 6276-6279 | Seven
years after Hertz, Jagdish Chandra Bose, working at
Calcutta (now Kolkata), succeeded in producing and
observing electromagnetic waves of much shorter
wavelength (25 mm to 5 mm) His experiment, like that
of Hertz’s, was confined to the laboratory At around the same time, Guglielmo Marconi in Italy
followed Hertz’s work and succeeded in transmitting
electromagnetic waves over distances of many kilometres Marconi’s experiment marks the beginning of the field of
communication using electromagnetic waves |
1 | 6277-6280 | His experiment, like that
of Hertz’s, was confined to the laboratory At around the same time, Guglielmo Marconi in Italy
followed Hertz’s work and succeeded in transmitting
electromagnetic waves over distances of many kilometres Marconi’s experiment marks the beginning of the field of
communication using electromagnetic waves 8 |
1 | 6278-6281 | At around the same time, Guglielmo Marconi in Italy
followed Hertz’s work and succeeded in transmitting
electromagnetic waves over distances of many kilometres Marconi’s experiment marks the beginning of the field of
communication using electromagnetic waves 8 3 |
1 | 6279-6282 | Marconi’s experiment marks the beginning of the field of
communication using electromagnetic waves 8 3 2 Nature of electromagnetic waves
It can be shown from Maxwell’s equations that electric
and magnetic fields in an electromagnetic wave are
perpendicular to each other, and to the direction of
propagation |
1 | 6280-6283 | 8 3 2 Nature of electromagnetic waves
It can be shown from Maxwell’s equations that electric
and magnetic fields in an electromagnetic wave are
perpendicular to each other, and to the direction of
propagation It appears reasonable, say from our
discussion of the displacement current |
1 | 6281-6284 | 3 2 Nature of electromagnetic waves
It can be shown from Maxwell’s equations that electric
and magnetic fields in an electromagnetic wave are
perpendicular to each other, and to the direction of
propagation It appears reasonable, say from our
discussion of the displacement current Consider
Fig |
1 | 6282-6285 | 2 Nature of electromagnetic waves
It can be shown from Maxwell’s equations that electric
and magnetic fields in an electromagnetic wave are
perpendicular to each other, and to the direction of
propagation It appears reasonable, say from our
discussion of the displacement current Consider
Fig 8 |
1 | 6283-6286 | It appears reasonable, say from our
discussion of the displacement current Consider
Fig 8 2 |
1 | 6284-6287 | Consider
Fig 8 2 The electric field inside the plates of the capacitor
is directed perpendicular to the plates |
1 | 6285-6288 | 8 2 The electric field inside the plates of the capacitor
is directed perpendicular to the plates The magnetic
field this gives rise to via the displacement current is
along the perimeter of a circle parallel to the capacitor
plates |
1 | 6286-6289 | 2 The electric field inside the plates of the capacitor
is directed perpendicular to the plates The magnetic
field this gives rise to via the displacement current is
along the perimeter of a circle parallel to the capacitor
plates So B and E are perpendicular in this case |
1 | 6287-6290 | The electric field inside the plates of the capacitor
is directed perpendicular to the plates The magnetic
field this gives rise to via the displacement current is
along the perimeter of a circle parallel to the capacitor
plates So B and E are perpendicular in this case This
is a general feature |
1 | 6288-6291 | The magnetic
field this gives rise to via the displacement current is
along the perimeter of a circle parallel to the capacitor
plates So B and E are perpendicular in this case This
is a general feature In Fig |
1 | 6289-6292 | So B and E are perpendicular in this case This
is a general feature In Fig 8 |
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