Chapter
stringclasses 18
values | sentence_range
stringlengths 3
9
| Text
stringlengths 7
7.34k
|
|---|---|---|
1 | 1990-1993 | Rationalised 2023-24
Physics
66
In an external electric field, the
positive and negative charges of a non-
polar molecule are displaced in opposite
directions The displacement stops when
the external force on the constituent
charges of the molecule is balanced by
the restoring force (due to internal fields
in the molecule) The non-polar molecule
thus develops an induced dipole moment The dielectric is said to be polarised by
the external field |
1 | 1991-1994 | The displacement stops when
the external force on the constituent
charges of the molecule is balanced by
the restoring force (due to internal fields
in the molecule) The non-polar molecule
thus develops an induced dipole moment The dielectric is said to be polarised by
the external field We consider only the
simple situation when the induced dipole
moment is in the direction of the field and
is proportional to the field strength |
1 | 1992-1995 | The non-polar molecule
thus develops an induced dipole moment The dielectric is said to be polarised by
the external field We consider only the
simple situation when the induced dipole
moment is in the direction of the field and
is proportional to the field strength (Substances for which this assumption
is true are called linear isotropic
dielectrics |
1 | 1993-1996 | The dielectric is said to be polarised by
the external field We consider only the
simple situation when the induced dipole
moment is in the direction of the field and
is proportional to the field strength (Substances for which this assumption
is true are called linear isotropic
dielectrics ) The induced dipole moments
of different molecules add up giving a net
dipole moment of the dielectric in the
presence of the external field |
1 | 1994-1997 | We consider only the
simple situation when the induced dipole
moment is in the direction of the field and
is proportional to the field strength (Substances for which this assumption
is true are called linear isotropic
dielectrics ) The induced dipole moments
of different molecules add up giving a net
dipole moment of the dielectric in the
presence of the external field A dielectric with polar molecules also
develops a net dipole moment in an
external field, but for a different reason |
1 | 1995-1998 | (Substances for which this assumption
is true are called linear isotropic
dielectrics ) The induced dipole moments
of different molecules add up giving a net
dipole moment of the dielectric in the
presence of the external field A dielectric with polar molecules also
develops a net dipole moment in an
external field, but for a different reason In the absence of any external field, the
different permanent dipoles are oriented
randomly due to thermal agitation; so
the total dipole moment is zero |
1 | 1996-1999 | ) The induced dipole moments
of different molecules add up giving a net
dipole moment of the dielectric in the
presence of the external field A dielectric with polar molecules also
develops a net dipole moment in an
external field, but for a different reason In the absence of any external field, the
different permanent dipoles are oriented
randomly due to thermal agitation; so
the total dipole moment is zero When
an external field is applied, the individual dipole moments tend to align
with the field |
1 | 1997-2000 | A dielectric with polar molecules also
develops a net dipole moment in an
external field, but for a different reason In the absence of any external field, the
different permanent dipoles are oriented
randomly due to thermal agitation; so
the total dipole moment is zero When
an external field is applied, the individual dipole moments tend to align
with the field When summed overall the molecules, there is then a net
dipole moment in the direction of the external field, i |
1 | 1998-2001 | In the absence of any external field, the
different permanent dipoles are oriented
randomly due to thermal agitation; so
the total dipole moment is zero When
an external field is applied, the individual dipole moments tend to align
with the field When summed overall the molecules, there is then a net
dipole moment in the direction of the external field, i e |
1 | 1999-2002 | When
an external field is applied, the individual dipole moments tend to align
with the field When summed overall the molecules, there is then a net
dipole moment in the direction of the external field, i e , the dielectric is
polarised |
1 | 2000-2003 | When summed overall the molecules, there is then a net
dipole moment in the direction of the external field, i e , the dielectric is
polarised The extent of polarisation depends on the relative strength of
two mutually opposite factors: the dipole potential energy in the external
field tending to align the dipoles with the field and thermal energy tending
to disrupt the alignment |
1 | 2001-2004 | e , the dielectric is
polarised The extent of polarisation depends on the relative strength of
two mutually opposite factors: the dipole potential energy in the external
field tending to align the dipoles with the field and thermal energy tending
to disrupt the alignment There may be, in addition, the ‘induced dipole
moment’ effect as for non-polar molecules, but generally the alignment
effect is more important for polar molecules |
1 | 2002-2005 | , the dielectric is
polarised The extent of polarisation depends on the relative strength of
two mutually opposite factors: the dipole potential energy in the external
field tending to align the dipoles with the field and thermal energy tending
to disrupt the alignment There may be, in addition, the ‘induced dipole
moment’ effect as for non-polar molecules, but generally the alignment
effect is more important for polar molecules Thus in either case, whether polar or non-polar, a dielectric develops
a net dipole moment in the presence of an external field |
1 | 2003-2006 | The extent of polarisation depends on the relative strength of
two mutually opposite factors: the dipole potential energy in the external
field tending to align the dipoles with the field and thermal energy tending
to disrupt the alignment There may be, in addition, the ‘induced dipole
moment’ effect as for non-polar molecules, but generally the alignment
effect is more important for polar molecules Thus in either case, whether polar or non-polar, a dielectric develops
a net dipole moment in the presence of an external field The dipole
moment per unit volume is called polarisation and is denoted by P |
1 | 2004-2007 | There may be, in addition, the ‘induced dipole
moment’ effect as for non-polar molecules, but generally the alignment
effect is more important for polar molecules Thus in either case, whether polar or non-polar, a dielectric develops
a net dipole moment in the presence of an external field The dipole
moment per unit volume is called polarisation and is denoted by P For
linear isotropic dielectrics,
0
P=ε χ
eE
(2 |
1 | 2005-2008 | Thus in either case, whether polar or non-polar, a dielectric develops
a net dipole moment in the presence of an external field The dipole
moment per unit volume is called polarisation and is denoted by P For
linear isotropic dielectrics,
0
P=ε χ
eE
(2 37)
where ce is a constant characteristic of the dielectric and is known as the
electric susceptibility of the dielectric medium |
1 | 2006-2009 | The dipole
moment per unit volume is called polarisation and is denoted by P For
linear isotropic dielectrics,
0
P=ε χ
eE
(2 37)
where ce is a constant characteristic of the dielectric and is known as the
electric susceptibility of the dielectric medium It is possible to relate ce to the molecular properties of the substance,
but we shall not pursue that here |
1 | 2007-2010 | For
linear isotropic dielectrics,
0
P=ε χ
eE
(2 37)
where ce is a constant characteristic of the dielectric and is known as the
electric susceptibility of the dielectric medium It is possible to relate ce to the molecular properties of the substance,
but we shall not pursue that here The question is: how does the polarised dielectric modify the original
external field inside it |
1 | 2008-2011 | 37)
where ce is a constant characteristic of the dielectric and is known as the
electric susceptibility of the dielectric medium It is possible to relate ce to the molecular properties of the substance,
but we shall not pursue that here The question is: how does the polarised dielectric modify the original
external field inside it Let us consider, for simplicity, a rectangular
dielectric slab placed in a uniform external field E0 parallel to two of its
faces |
1 | 2009-2012 | It is possible to relate ce to the molecular properties of the substance,
but we shall not pursue that here The question is: how does the polarised dielectric modify the original
external field inside it Let us consider, for simplicity, a rectangular
dielectric slab placed in a uniform external field E0 parallel to two of its
faces The field causes a uniform polarisation P of the dielectric |
1 | 2010-2013 | The question is: how does the polarised dielectric modify the original
external field inside it Let us consider, for simplicity, a rectangular
dielectric slab placed in a uniform external field E0 parallel to two of its
faces The field causes a uniform polarisation P of the dielectric Thus
FIGURE 2 |
1 | 2011-2014 | Let us consider, for simplicity, a rectangular
dielectric slab placed in a uniform external field E0 parallel to two of its
faces The field causes a uniform polarisation P of the dielectric Thus
FIGURE 2 22 A dielectric develops a net dipole
moment in an external electric field |
1 | 2012-2015 | The field causes a uniform polarisation P of the dielectric Thus
FIGURE 2 22 A dielectric develops a net dipole
moment in an external electric field (a) Non-polar
molecules, (b) Polar molecules |
1 | 2013-2016 | Thus
FIGURE 2 22 A dielectric develops a net dipole
moment in an external electric field (a) Non-polar
molecules, (b) Polar molecules Rationalised 2023-24
Electrostatic Potential
and Capacitance
67
every volume element Dv of the slab has a dipole moment
P Dv in the direction of the field |
1 | 2014-2017 | 22 A dielectric develops a net dipole
moment in an external electric field (a) Non-polar
molecules, (b) Polar molecules Rationalised 2023-24
Electrostatic Potential
and Capacitance
67
every volume element Dv of the slab has a dipole moment
P Dv in the direction of the field The volume element Dv is
macroscopically small but contains a very large number of
molecular dipoles |
1 | 2015-2018 | (a) Non-polar
molecules, (b) Polar molecules Rationalised 2023-24
Electrostatic Potential
and Capacitance
67
every volume element Dv of the slab has a dipole moment
P Dv in the direction of the field The volume element Dv is
macroscopically small but contains a very large number of
molecular dipoles Anywhere inside the dielectric, the
volume element Dv has no net charge (though it has net
dipole moment) |
1 | 2016-2019 | Rationalised 2023-24
Electrostatic Potential
and Capacitance
67
every volume element Dv of the slab has a dipole moment
P Dv in the direction of the field The volume element Dv is
macroscopically small but contains a very large number of
molecular dipoles Anywhere inside the dielectric, the
volume element Dv has no net charge (though it has net
dipole moment) This is, because, the positive charge of one
dipole sits close to the negative charge of the adjacent dipole |
1 | 2017-2020 | The volume element Dv is
macroscopically small but contains a very large number of
molecular dipoles Anywhere inside the dielectric, the
volume element Dv has no net charge (though it has net
dipole moment) This is, because, the positive charge of one
dipole sits close to the negative charge of the adjacent dipole However, at the surfaces of the dielectric normal to the
electric field, there is evidently a net charge density |
1 | 2018-2021 | Anywhere inside the dielectric, the
volume element Dv has no net charge (though it has net
dipole moment) This is, because, the positive charge of one
dipole sits close to the negative charge of the adjacent dipole However, at the surfaces of the dielectric normal to the
electric field, there is evidently a net charge density As seen
in Fig 2 |
1 | 2019-2022 | This is, because, the positive charge of one
dipole sits close to the negative charge of the adjacent dipole However, at the surfaces of the dielectric normal to the
electric field, there is evidently a net charge density As seen
in Fig 2 23, the positive ends of the dipoles remain
unneutralised at the right surface and the negative ends at
the left surface |
1 | 2020-2023 | However, at the surfaces of the dielectric normal to the
electric field, there is evidently a net charge density As seen
in Fig 2 23, the positive ends of the dipoles remain
unneutralised at the right surface and the negative ends at
the left surface The unbalanced charges are the induced
charges due to the external field |
1 | 2021-2024 | As seen
in Fig 2 23, the positive ends of the dipoles remain
unneutralised at the right surface and the negative ends at
the left surface The unbalanced charges are the induced
charges due to the external field Thus, the polarised dielectric is equivalent to two charged
surfaces with induced surface charge densities, say sp
and –sp |
1 | 2022-2025 | 23, the positive ends of the dipoles remain
unneutralised at the right surface and the negative ends at
the left surface The unbalanced charges are the induced
charges due to the external field Thus, the polarised dielectric is equivalent to two charged
surfaces with induced surface charge densities, say sp
and –sp Clearly, the field produced by these surface charges
opposes the external field |
1 | 2023-2026 | The unbalanced charges are the induced
charges due to the external field Thus, the polarised dielectric is equivalent to two charged
surfaces with induced surface charge densities, say sp
and –sp Clearly, the field produced by these surface charges
opposes the external field The total field in the dielectric
is, thereby, reduced from the case when no dielectric is
present |
1 | 2024-2027 | Thus, the polarised dielectric is equivalent to two charged
surfaces with induced surface charge densities, say sp
and –sp Clearly, the field produced by these surface charges
opposes the external field The total field in the dielectric
is, thereby, reduced from the case when no dielectric is
present We should note that the surface charge density
±sp arises from bound (not free charges) in the dielectric |
1 | 2025-2028 | Clearly, the field produced by these surface charges
opposes the external field The total field in the dielectric
is, thereby, reduced from the case when no dielectric is
present We should note that the surface charge density
±sp arises from bound (not free charges) in the dielectric 2 |
1 | 2026-2029 | The total field in the dielectric
is, thereby, reduced from the case when no dielectric is
present We should note that the surface charge density
±sp arises from bound (not free charges) in the dielectric 2 11 CAPACITORS AND CAPACITANCE
A capacitor is a system of two conductors separated by an insulator
(Fig |
1 | 2027-2030 | We should note that the surface charge density
±sp arises from bound (not free charges) in the dielectric 2 11 CAPACITORS AND CAPACITANCE
A capacitor is a system of two conductors separated by an insulator
(Fig 2 |
1 | 2028-2031 | 2 11 CAPACITORS AND CAPACITANCE
A capacitor is a system of two conductors separated by an insulator
(Fig 2 24) |
1 | 2029-2032 | 11 CAPACITORS AND CAPACITANCE
A capacitor is a system of two conductors separated by an insulator
(Fig 2 24) The conductors have charges, say Q1 and Q2, and potentials
V1 and V2 |
1 | 2030-2033 | 2 24) The conductors have charges, say Q1 and Q2, and potentials
V1 and V2 Usually, in practice, the two conductors have charges Q
and – Q, with potential difference V = V1 – V2 between them |
1 | 2031-2034 | 24) The conductors have charges, say Q1 and Q2, and potentials
V1 and V2 Usually, in practice, the two conductors have charges Q
and – Q, with potential difference V = V1 – V2 between them We shall
consider only this kind of charge configuration of the capacitor |
1 | 2032-2035 | The conductors have charges, say Q1 and Q2, and potentials
V1 and V2 Usually, in practice, the two conductors have charges Q
and – Q, with potential difference V = V1 – V2 between them We shall
consider only this kind of charge configuration of the capacitor (Even a
single conductor can be used as a capacitor by assuming the other at
infinity |
1 | 2033-2036 | Usually, in practice, the two conductors have charges Q
and – Q, with potential difference V = V1 – V2 between them We shall
consider only this kind of charge configuration of the capacitor (Even a
single conductor can be used as a capacitor by assuming the other at
infinity ) The conductors may be so charged by connecting them to the
two terminals of a battery |
1 | 2034-2037 | We shall
consider only this kind of charge configuration of the capacitor (Even a
single conductor can be used as a capacitor by assuming the other at
infinity ) The conductors may be so charged by connecting them to the
two terminals of a battery Q is called the charge of the capacitor, though
this, in fact, is the charge on one of the conductors – the total charge of
the capacitor is zero |
1 | 2035-2038 | (Even a
single conductor can be used as a capacitor by assuming the other at
infinity ) The conductors may be so charged by connecting them to the
two terminals of a battery Q is called the charge of the capacitor, though
this, in fact, is the charge on one of the conductors – the total charge of
the capacitor is zero The electric field in the region between the
conductors is proportional to the charge Q |
1 | 2036-2039 | ) The conductors may be so charged by connecting them to the
two terminals of a battery Q is called the charge of the capacitor, though
this, in fact, is the charge on one of the conductors – the total charge of
the capacitor is zero The electric field in the region between the
conductors is proportional to the charge Q That
is, if the charge on the capacitor is, say doubled,
the electric field will also be doubled at every point |
1 | 2037-2040 | Q is called the charge of the capacitor, though
this, in fact, is the charge on one of the conductors – the total charge of
the capacitor is zero The electric field in the region between the
conductors is proportional to the charge Q That
is, if the charge on the capacitor is, say doubled,
the electric field will also be doubled at every point (This follows from the direct proportionality
between field and charge implied by Coulomb’s
law and the superposition principle |
1 | 2038-2041 | The electric field in the region between the
conductors is proportional to the charge Q That
is, if the charge on the capacitor is, say doubled,
the electric field will also be doubled at every point (This follows from the direct proportionality
between field and charge implied by Coulomb’s
law and the superposition principle ) Now,
potential difference V is the work done per unit
positive charge in taking a small test charge from
the conductor 2 to 1 against the field |
1 | 2039-2042 | That
is, if the charge on the capacitor is, say doubled,
the electric field will also be doubled at every point (This follows from the direct proportionality
between field and charge implied by Coulomb’s
law and the superposition principle ) Now,
potential difference V is the work done per unit
positive charge in taking a small test charge from
the conductor 2 to 1 against the field Consequently, V is also proportional to Q, and the
ratio Q/V is a constant:
Q
C
=V
(2 |
1 | 2040-2043 | (This follows from the direct proportionality
between field and charge implied by Coulomb’s
law and the superposition principle ) Now,
potential difference V is the work done per unit
positive charge in taking a small test charge from
the conductor 2 to 1 against the field Consequently, V is also proportional to Q, and the
ratio Q/V is a constant:
Q
C
=V
(2 38)
The constant C is called the capacitance of the capacitor |
1 | 2041-2044 | ) Now,
potential difference V is the work done per unit
positive charge in taking a small test charge from
the conductor 2 to 1 against the field Consequently, V is also proportional to Q, and the
ratio Q/V is a constant:
Q
C
=V
(2 38)
The constant C is called the capacitance of the capacitor C is independent
of Q or V, as stated above |
1 | 2042-2045 | Consequently, V is also proportional to Q, and the
ratio Q/V is a constant:
Q
C
=V
(2 38)
The constant C is called the capacitance of the capacitor C is independent
of Q or V, as stated above The capacitance C depends only on the
FIGURE 2 |
1 | 2043-2046 | 38)
The constant C is called the capacitance of the capacitor C is independent
of Q or V, as stated above The capacitance C depends only on the
FIGURE 2 23 A uniformly
polarised dielectric amounts
to induced surface charge
density, but no volume
charge density |
1 | 2044-2047 | C is independent
of Q or V, as stated above The capacitance C depends only on the
FIGURE 2 23 A uniformly
polarised dielectric amounts
to induced surface charge
density, but no volume
charge density FIGURE 2 |
1 | 2045-2048 | The capacitance C depends only on the
FIGURE 2 23 A uniformly
polarised dielectric amounts
to induced surface charge
density, but no volume
charge density FIGURE 2 24 A system of two conductors
separated by an insulator forms a capacitor |
1 | 2046-2049 | 23 A uniformly
polarised dielectric amounts
to induced surface charge
density, but no volume
charge density FIGURE 2 24 A system of two conductors
separated by an insulator forms a capacitor Rationalised 2023-24
Physics
68
geometrical configuration (shape, size, separation) of the system of two
conductors |
1 | 2047-2050 | FIGURE 2 24 A system of two conductors
separated by an insulator forms a capacitor Rationalised 2023-24
Physics
68
geometrical configuration (shape, size, separation) of the system of two
conductors [As we shall see later, it also depends on the nature of the
insulator (dielectric) separating the two conductors |
1 | 2048-2051 | 24 A system of two conductors
separated by an insulator forms a capacitor Rationalised 2023-24
Physics
68
geometrical configuration (shape, size, separation) of the system of two
conductors [As we shall see later, it also depends on the nature of the
insulator (dielectric) separating the two conductors ] The SI unit of
capacitance is 1 farad (=1 coulomb volt-1) or 1 F = 1 C V–1 |
1 | 2049-2052 | Rationalised 2023-24
Physics
68
geometrical configuration (shape, size, separation) of the system of two
conductors [As we shall see later, it also depends on the nature of the
insulator (dielectric) separating the two conductors ] The SI unit of
capacitance is 1 farad (=1 coulomb volt-1) or 1 F = 1 C V–1 A capacitor
with fixed capacitance is symbolically shown as ---||---, while the one with
variable capacitance is shown as |
1 | 2050-2053 | [As we shall see later, it also depends on the nature of the
insulator (dielectric) separating the two conductors ] The SI unit of
capacitance is 1 farad (=1 coulomb volt-1) or 1 F = 1 C V–1 A capacitor
with fixed capacitance is symbolically shown as ---||---, while the one with
variable capacitance is shown as Equation (2 |
1 | 2051-2054 | ] The SI unit of
capacitance is 1 farad (=1 coulomb volt-1) or 1 F = 1 C V–1 A capacitor
with fixed capacitance is symbolically shown as ---||---, while the one with
variable capacitance is shown as Equation (2 38) shows that for large C, V is small for a given Q |
1 | 2052-2055 | A capacitor
with fixed capacitance is symbolically shown as ---||---, while the one with
variable capacitance is shown as Equation (2 38) shows that for large C, V is small for a given Q This
means a capacitor with large capacitance can hold large amount of charge
Q at a relatively small V |
1 | 2053-2056 | Equation (2 38) shows that for large C, V is small for a given Q This
means a capacitor with large capacitance can hold large amount of charge
Q at a relatively small V This is of practical importance |
1 | 2054-2057 | 38) shows that for large C, V is small for a given Q This
means a capacitor with large capacitance can hold large amount of charge
Q at a relatively small V This is of practical importance High potential
difference implies strong electric field around the conductors |
1 | 2055-2058 | This
means a capacitor with large capacitance can hold large amount of charge
Q at a relatively small V This is of practical importance High potential
difference implies strong electric field around the conductors A strong
electric field can ionise the surrounding air and accelerate the charges so
produced to the oppositely charged plates, thereby neutralising the charge
on the capacitor plates, at least partly |
1 | 2056-2059 | This is of practical importance High potential
difference implies strong electric field around the conductors A strong
electric field can ionise the surrounding air and accelerate the charges so
produced to the oppositely charged plates, thereby neutralising the charge
on the capacitor plates, at least partly In other words, the charge of the
capacitor leaks away due to the reduction in insulating power of the
intervening medium |
1 | 2057-2060 | High potential
difference implies strong electric field around the conductors A strong
electric field can ionise the surrounding air and accelerate the charges so
produced to the oppositely charged plates, thereby neutralising the charge
on the capacitor plates, at least partly In other words, the charge of the
capacitor leaks away due to the reduction in insulating power of the
intervening medium The maximum electric field that a dielectric medium can withstand
without break-down (of its insulating property) is called its dielectric
strength; for air it is about 3 × 106 Vm–1 |
1 | 2058-2061 | A strong
electric field can ionise the surrounding air and accelerate the charges so
produced to the oppositely charged plates, thereby neutralising the charge
on the capacitor plates, at least partly In other words, the charge of the
capacitor leaks away due to the reduction in insulating power of the
intervening medium The maximum electric field that a dielectric medium can withstand
without break-down (of its insulating property) is called its dielectric
strength; for air it is about 3 × 106 Vm–1 For a separation between
conductors of the order of 1 cm or so, this field corresponds to a potential
difference of 3 × 104 V between the conductors |
1 | 2059-2062 | In other words, the charge of the
capacitor leaks away due to the reduction in insulating power of the
intervening medium The maximum electric field that a dielectric medium can withstand
without break-down (of its insulating property) is called its dielectric
strength; for air it is about 3 × 106 Vm–1 For a separation between
conductors of the order of 1 cm or so, this field corresponds to a potential
difference of 3 × 104 V between the conductors Thus, for a capacitor to
store a large amount of charge without leaking, its capacitance should
be high enough so that the potential difference and hence the electric
field do not exceed the break-down limits |
1 | 2060-2063 | The maximum electric field that a dielectric medium can withstand
without break-down (of its insulating property) is called its dielectric
strength; for air it is about 3 × 106 Vm–1 For a separation between
conductors of the order of 1 cm or so, this field corresponds to a potential
difference of 3 × 104 V between the conductors Thus, for a capacitor to
store a large amount of charge without leaking, its capacitance should
be high enough so that the potential difference and hence the electric
field do not exceed the break-down limits Put differently, there is a limit
to the amount of charge that can be stored on a given capacitor without
significant leaking |
1 | 2061-2064 | For a separation between
conductors of the order of 1 cm or so, this field corresponds to a potential
difference of 3 × 104 V between the conductors Thus, for a capacitor to
store a large amount of charge without leaking, its capacitance should
be high enough so that the potential difference and hence the electric
field do not exceed the break-down limits Put differently, there is a limit
to the amount of charge that can be stored on a given capacitor without
significant leaking In practice, a farad is a very big unit; the most common
units are its sub-multiples 1 mF = 10–6 F, 1 nF = 10–9 F, 1 pF = 10–12 F,
etc |
1 | 2062-2065 | Thus, for a capacitor to
store a large amount of charge without leaking, its capacitance should
be high enough so that the potential difference and hence the electric
field do not exceed the break-down limits Put differently, there is a limit
to the amount of charge that can be stored on a given capacitor without
significant leaking In practice, a farad is a very big unit; the most common
units are its sub-multiples 1 mF = 10–6 F, 1 nF = 10–9 F, 1 pF = 10–12 F,
etc Besides its use in storing charge, a capacitor is a key element of most
ac circuits with important functions, as described in Chapter 7 |
1 | 2063-2066 | Put differently, there is a limit
to the amount of charge that can be stored on a given capacitor without
significant leaking In practice, a farad is a very big unit; the most common
units are its sub-multiples 1 mF = 10–6 F, 1 nF = 10–9 F, 1 pF = 10–12 F,
etc Besides its use in storing charge, a capacitor is a key element of most
ac circuits with important functions, as described in Chapter 7 2 |
1 | 2064-2067 | In practice, a farad is a very big unit; the most common
units are its sub-multiples 1 mF = 10–6 F, 1 nF = 10–9 F, 1 pF = 10–12 F,
etc Besides its use in storing charge, a capacitor is a key element of most
ac circuits with important functions, as described in Chapter 7 2 12 THE PARALLEL PLATE CAPACITOR
A parallel plate capacitor consists of two large plane parallel conducting
plates separated by a small distance (Fig |
1 | 2065-2068 | Besides its use in storing charge, a capacitor is a key element of most
ac circuits with important functions, as described in Chapter 7 2 12 THE PARALLEL PLATE CAPACITOR
A parallel plate capacitor consists of two large plane parallel conducting
plates separated by a small distance (Fig 2 |
1 | 2066-2069 | 2 12 THE PARALLEL PLATE CAPACITOR
A parallel plate capacitor consists of two large plane parallel conducting
plates separated by a small distance (Fig 2 25) |
1 | 2067-2070 | 12 THE PARALLEL PLATE CAPACITOR
A parallel plate capacitor consists of two large plane parallel conducting
plates separated by a small distance (Fig 2 25) We first take the
intervening medium between the plates to be
vacuum |
1 | 2068-2071 | 2 25) We first take the
intervening medium between the plates to be
vacuum The effect of a dielectric medium between
the plates is discussed in the next section |
1 | 2069-2072 | 25) We first take the
intervening medium between the plates to be
vacuum The effect of a dielectric medium between
the plates is discussed in the next section Let A be
the area of each plate and d the separation between
them |
1 | 2070-2073 | We first take the
intervening medium between the plates to be
vacuum The effect of a dielectric medium between
the plates is discussed in the next section Let A be
the area of each plate and d the separation between
them The two plates have charges Q and –Q |
1 | 2071-2074 | The effect of a dielectric medium between
the plates is discussed in the next section Let A be
the area of each plate and d the separation between
them The two plates have charges Q and –Q Since
d is much smaller than the linear dimension of the
plates (d2 << A), we can use the result on electric
field by an infinite plane sheet of uniform surface
charge density (Section 1 |
1 | 2072-2075 | Let A be
the area of each plate and d the separation between
them The two plates have charges Q and –Q Since
d is much smaller than the linear dimension of the
plates (d2 << A), we can use the result on electric
field by an infinite plane sheet of uniform surface
charge density (Section 1 15) |
1 | 2073-2076 | The two plates have charges Q and –Q Since
d is much smaller than the linear dimension of the
plates (d2 << A), we can use the result on electric
field by an infinite plane sheet of uniform surface
charge density (Section 1 15) Plate 1 has surface
charge density s = Q/A and plate 2 has a surface
charge density –s |
1 | 2074-2077 | Since
d is much smaller than the linear dimension of the
plates (d2 << A), we can use the result on electric
field by an infinite plane sheet of uniform surface
charge density (Section 1 15) Plate 1 has surface
charge density s = Q/A and plate 2 has a surface
charge density –s Using Eq |
1 | 2075-2078 | 15) Plate 1 has surface
charge density s = Q/A and plate 2 has a surface
charge density –s Using Eq (1 |
1 | 2076-2079 | Plate 1 has surface
charge density s = Q/A and plate 2 has a surface
charge density –s Using Eq (1 33), the electric field
in different regions is:
Outer region I (region above the plate 1),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 |
1 | 2077-2080 | Using Eq (1 33), the electric field
in different regions is:
Outer region I (region above the plate 1),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 39)
FIGURE 2 |
1 | 2078-2081 | (1 33), the electric field
in different regions is:
Outer region I (region above the plate 1),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 39)
FIGURE 2 25 The parallel plate capacitor |
1 | 2079-2082 | 33), the electric field
in different regions is:
Outer region I (region above the plate 1),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 39)
FIGURE 2 25 The parallel plate capacitor Rationalised 2023-24
Electrostatic Potential
and Capacitance
69
Outer region II (region below the plate 2),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 |
1 | 2080-2083 | 39)
FIGURE 2 25 The parallel plate capacitor Rationalised 2023-24
Electrostatic Potential
and Capacitance
69
Outer region II (region below the plate 2),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 40)
In the inner region between the plates 1 and 2, the electric fields due
to the two charged plates add up, giving
0
0
0
0
2
2
Q
E
A
σ
σ
σ
ε
ε
ε
ε
=
+
=
=
(2 |
1 | 2081-2084 | 25 The parallel plate capacitor Rationalised 2023-24
Electrostatic Potential
and Capacitance
69
Outer region II (region below the plate 2),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 40)
In the inner region between the plates 1 and 2, the electric fields due
to the two charged plates add up, giving
0
0
0
0
2
2
Q
E
A
σ
σ
σ
ε
ε
ε
ε
=
+
=
=
(2 41)
The direction of electric field is from the positive to the negative plate |
1 | 2082-2085 | Rationalised 2023-24
Electrostatic Potential
and Capacitance
69
Outer region II (region below the plate 2),
0
0
0
2
2
E
σ
σ
ε
ε
=
−
=
(2 40)
In the inner region between the plates 1 and 2, the electric fields due
to the two charged plates add up, giving
0
0
0
0
2
2
Q
E
A
σ
σ
σ
ε
ε
ε
ε
=
+
=
=
(2 41)
The direction of electric field is from the positive to the negative plate Thus, the electric field is localised between the two plates and is
uniform throughout |
1 | 2083-2086 | 40)
In the inner region between the plates 1 and 2, the electric fields due
to the two charged plates add up, giving
0
0
0
0
2
2
Q
E
A
σ
σ
σ
ε
ε
ε
ε
=
+
=
=
(2 41)
The direction of electric field is from the positive to the negative plate Thus, the electric field is localised between the two plates and is
uniform throughout For plates with finite area, this will not be true near
the outer boundaries of the plates |
1 | 2084-2087 | 41)
The direction of electric field is from the positive to the negative plate Thus, the electric field is localised between the two plates and is
uniform throughout For plates with finite area, this will not be true near
the outer boundaries of the plates The field lines bend outward at the
edges — an effect called ‘fringing of the field’ |
1 | 2085-2088 | Thus, the electric field is localised between the two plates and is
uniform throughout For plates with finite area, this will not be true near
the outer boundaries of the plates The field lines bend outward at the
edges — an effect called ‘fringing of the field’ By the same token, s will
not be strictly uniform on the entire plate |
1 | 2086-2089 | For plates with finite area, this will not be true near
the outer boundaries of the plates The field lines bend outward at the
edges — an effect called ‘fringing of the field’ By the same token, s will
not be strictly uniform on the entire plate [E and s are related by Eq |
1 | 2087-2090 | The field lines bend outward at the
edges — an effect called ‘fringing of the field’ By the same token, s will
not be strictly uniform on the entire plate [E and s are related by Eq (2 |
1 | 2088-2091 | By the same token, s will
not be strictly uniform on the entire plate [E and s are related by Eq (2 35) |
1 | 2089-2092 | [E and s are related by Eq (2 35) ] However, for d2 << A, these effects can be ignored in the regions
sufficiently far from the edges, and the field there is given by Eq |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.