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1 | 1190-1193 | (iii) Electrostatic field lines start at positive charges and
end at negative charges —they cannot form closed loops 11 An electric dipole is a pair of equal and opposite charges q and –q
separated by some distance 2a Its dipole moment vector p has
magnitude 2qa and is in the direction of the dipole axis from –q to q |
1 | 1191-1194 | 11 An electric dipole is a pair of equal and opposite charges q and –q
separated by some distance 2a Its dipole moment vector p has
magnitude 2qa and is in the direction of the dipole axis from –q to q Rationalised 2023-24
Electric Charges
and Fields
39
12 |
1 | 1192-1195 | An electric dipole is a pair of equal and opposite charges q and –q
separated by some distance 2a Its dipole moment vector p has
magnitude 2qa and is in the direction of the dipole axis from –q to q Rationalised 2023-24
Electric Charges
and Fields
39
12 Field of an electric dipole in its equatorial plane (i |
1 | 1193-1196 | Its dipole moment vector p has
magnitude 2qa and is in the direction of the dipole axis from –q to q Rationalised 2023-24
Electric Charges
and Fields
39
12 Field of an electric dipole in its equatorial plane (i e |
1 | 1194-1197 | Rationalised 2023-24
Electric Charges
and Fields
39
12 Field of an electric dipole in its equatorial plane (i e , the plane
perpendicular to its axis and passing through its centre) at a distance
r from the centre:
2
2 3/2
1
4
(
)
o
a
r
ε
−
=
π
+
p
E
3 ,
4
o
for r
a
−εr
≅
>>
π
p
Dipole electric field on the axis at a distance r from the centre:
2
2 2
0
2
4
(
)
r
r
a
ε
=
π
p−
E
3
0
42
for
r
a
εr
≅
>>
π
p
The 1/r3 dependence of dipole electric fields should be noted in contrast
to the 1/r 2 dependence of electric field due to a point charge |
1 | 1195-1198 | Field of an electric dipole in its equatorial plane (i e , the plane
perpendicular to its axis and passing through its centre) at a distance
r from the centre:
2
2 3/2
1
4
(
)
o
a
r
ε
−
=
π
+
p
E
3 ,
4
o
for r
a
−εr
≅
>>
π
p
Dipole electric field on the axis at a distance r from the centre:
2
2 2
0
2
4
(
)
r
r
a
ε
=
π
p−
E
3
0
42
for
r
a
εr
≅
>>
π
p
The 1/r3 dependence of dipole electric fields should be noted in contrast
to the 1/r 2 dependence of electric field due to a point charge 13 |
1 | 1196-1199 | e , the plane
perpendicular to its axis and passing through its centre) at a distance
r from the centre:
2
2 3/2
1
4
(
)
o
a
r
ε
−
=
π
+
p
E
3 ,
4
o
for r
a
−εr
≅
>>
π
p
Dipole electric field on the axis at a distance r from the centre:
2
2 2
0
2
4
(
)
r
r
a
ε
=
π
p−
E
3
0
42
for
r
a
εr
≅
>>
π
p
The 1/r3 dependence of dipole electric fields should be noted in contrast
to the 1/r 2 dependence of electric field due to a point charge 13 In a uniform electric field E, a dipole experiences a torque τ given by
τ = p × E
but experiences no net force |
1 | 1197-1200 | , the plane
perpendicular to its axis and passing through its centre) at a distance
r from the centre:
2
2 3/2
1
4
(
)
o
a
r
ε
−
=
π
+
p
E
3 ,
4
o
for r
a
−εr
≅
>>
π
p
Dipole electric field on the axis at a distance r from the centre:
2
2 2
0
2
4
(
)
r
r
a
ε
=
π
p−
E
3
0
42
for
r
a
εr
≅
>>
π
p
The 1/r3 dependence of dipole electric fields should be noted in contrast
to the 1/r 2 dependence of electric field due to a point charge 13 In a uniform electric field E, a dipole experiences a torque τ given by
τ = p × E
but experiences no net force 14 |
1 | 1198-1201 | 13 In a uniform electric field E, a dipole experiences a torque τ given by
τ = p × E
but experiences no net force 14 The flux Df of electric field E through a small area element DS is
given by
Df = E |
1 | 1199-1202 | In a uniform electric field E, a dipole experiences a torque τ given by
τ = p × E
but experiences no net force 14 The flux Df of electric field E through a small area element DS is
given by
Df = E DS
The vector area element DS is
DS = DS ˆn
where DS is the magnitude of the area element and ˆn is normal to the
area element, which can be considered planar for sufficiently small DS |
1 | 1200-1203 | 14 The flux Df of electric field E through a small area element DS is
given by
Df = E DS
The vector area element DS is
DS = DS ˆn
where DS is the magnitude of the area element and ˆn is normal to the
area element, which can be considered planar for sufficiently small DS For an area element of a closed surface, ˆn is taken to be the direction
of outward normal, by convention |
1 | 1201-1204 | The flux Df of electric field E through a small area element DS is
given by
Df = E DS
The vector area element DS is
DS = DS ˆn
where DS is the magnitude of the area element and ˆn is normal to the
area element, which can be considered planar for sufficiently small DS For an area element of a closed surface, ˆn is taken to be the direction
of outward normal, by convention 15 |
1 | 1202-1205 | DS
The vector area element DS is
DS = DS ˆn
where DS is the magnitude of the area element and ˆn is normal to the
area element, which can be considered planar for sufficiently small DS For an area element of a closed surface, ˆn is taken to be the direction
of outward normal, by convention 15 Gauss’s law: The flux of electric field through any closed surface S is
1/e0 times the total charge enclosed by S |
1 | 1203-1206 | For an area element of a closed surface, ˆn is taken to be the direction
of outward normal, by convention 15 Gauss’s law: The flux of electric field through any closed surface S is
1/e0 times the total charge enclosed by S The law is especially useful
in determining electric field E, when the source distribution has simple
symmetry:
(i) Thin infinitely long straight wire of uniform linear charge density l
0
ˆ
2
r
ελ
=
π
E
n
where r is the perpendicular distance of the point from the wire and
ˆn is the radial unit vector in the plane normal to the wire passing
through the point |
1 | 1204-1207 | 15 Gauss’s law: The flux of electric field through any closed surface S is
1/e0 times the total charge enclosed by S The law is especially useful
in determining electric field E, when the source distribution has simple
symmetry:
(i) Thin infinitely long straight wire of uniform linear charge density l
0
ˆ
2
r
ελ
=
π
E
n
where r is the perpendicular distance of the point from the wire and
ˆn is the radial unit vector in the plane normal to the wire passing
through the point (ii) Infinite thin plane sheet of uniform surface charge density s
0
ˆ
2
σ
ε
E=
n
where ˆn is a unit vector normal to the plane, outward on either side |
1 | 1205-1208 | Gauss’s law: The flux of electric field through any closed surface S is
1/e0 times the total charge enclosed by S The law is especially useful
in determining electric field E, when the source distribution has simple
symmetry:
(i) Thin infinitely long straight wire of uniform linear charge density l
0
ˆ
2
r
ελ
=
π
E
n
where r is the perpendicular distance of the point from the wire and
ˆn is the radial unit vector in the plane normal to the wire passing
through the point (ii) Infinite thin plane sheet of uniform surface charge density s
0
ˆ
2
σ
ε
E=
n
where ˆn is a unit vector normal to the plane, outward on either side Rationalised 2023-24
40
Physics
(iii) Thin spherical shell of uniform surface charge density s
2
0
ˆ
(
)
4
q
r
R
r
ε
=
≥
π
E
r
E = 0
(r < R)
where r is the distance of the point from the centre of the shell and R
the radius of the shell |
1 | 1206-1209 | The law is especially useful
in determining electric field E, when the source distribution has simple
symmetry:
(i) Thin infinitely long straight wire of uniform linear charge density l
0
ˆ
2
r
ελ
=
π
E
n
where r is the perpendicular distance of the point from the wire and
ˆn is the radial unit vector in the plane normal to the wire passing
through the point (ii) Infinite thin plane sheet of uniform surface charge density s
0
ˆ
2
σ
ε
E=
n
where ˆn is a unit vector normal to the plane, outward on either side Rationalised 2023-24
40
Physics
(iii) Thin spherical shell of uniform surface charge density s
2
0
ˆ
(
)
4
q
r
R
r
ε
=
≥
π
E
r
E = 0
(r < R)
where r is the distance of the point from the centre of the shell and R
the radius of the shell q is the total charge of the shell: q = 4pR2s |
1 | 1207-1210 | (ii) Infinite thin plane sheet of uniform surface charge density s
0
ˆ
2
σ
ε
E=
n
where ˆn is a unit vector normal to the plane, outward on either side Rationalised 2023-24
40
Physics
(iii) Thin spherical shell of uniform surface charge density s
2
0
ˆ
(
)
4
q
r
R
r
ε
=
≥
π
E
r
E = 0
(r < R)
where r is the distance of the point from the centre of the shell and R
the radius of the shell q is the total charge of the shell: q = 4pR2s The electric field outside the shell is as though the total charge is
concentrated at the centre |
1 | 1208-1211 | Rationalised 2023-24
40
Physics
(iii) Thin spherical shell of uniform surface charge density s
2
0
ˆ
(
)
4
q
r
R
r
ε
=
≥
π
E
r
E = 0
(r < R)
where r is the distance of the point from the centre of the shell and R
the radius of the shell q is the total charge of the shell: q = 4pR2s The electric field outside the shell is as though the total charge is
concentrated at the centre The same result is true for a solid sphere
of uniform volume charge density |
1 | 1209-1212 | q is the total charge of the shell: q = 4pR2s The electric field outside the shell is as though the total charge is
concentrated at the centre The same result is true for a solid sphere
of uniform volume charge density The field is zero at all points inside
the shell |
1 | 1210-1213 | The electric field outside the shell is as though the total charge is
concentrated at the centre The same result is true for a solid sphere
of uniform volume charge density The field is zero at all points inside
the shell Physical quantity
Symbol
Dimensions
Unit
Remarks
Vector area element
D S
[L2]
m2
DS = DS ˆn
Electric field
E
[MLT–3A–1]
V m–1
Electric flux
f
[ML3 T–3A–1]
V m
Df = E |
1 | 1211-1214 | The same result is true for a solid sphere
of uniform volume charge density The field is zero at all points inside
the shell Physical quantity
Symbol
Dimensions
Unit
Remarks
Vector area element
D S
[L2]
m2
DS = DS ˆn
Electric field
E
[MLT–3A–1]
V m–1
Electric flux
f
[ML3 T–3A–1]
V m
Df = E DS
Dipole moment
p
[LTA]
C m
Vector directed
from negative to
positive charge
Charge density:
linear
l
[L–1 TA]
C m–1
Charge/length
surface
s
[L–2 TA]
C m–2
Charge/area
volume
r
[L–3 TA]
C m–3
Charge/volume
POINTS TO PONDER
1 |
1 | 1212-1215 | The field is zero at all points inside
the shell Physical quantity
Symbol
Dimensions
Unit
Remarks
Vector area element
D S
[L2]
m2
DS = DS ˆn
Electric field
E
[MLT–3A–1]
V m–1
Electric flux
f
[ML3 T–3A–1]
V m
Df = E DS
Dipole moment
p
[LTA]
C m
Vector directed
from negative to
positive charge
Charge density:
linear
l
[L–1 TA]
C m–1
Charge/length
surface
s
[L–2 TA]
C m–2
Charge/area
volume
r
[L–3 TA]
C m–3
Charge/volume
POINTS TO PONDER
1 You might wonder why the protons, all carrying positive charges,
are compactly residing inside the nucleus |
1 | 1213-1216 | Physical quantity
Symbol
Dimensions
Unit
Remarks
Vector area element
D S
[L2]
m2
DS = DS ˆn
Electric field
E
[MLT–3A–1]
V m–1
Electric flux
f
[ML3 T–3A–1]
V m
Df = E DS
Dipole moment
p
[LTA]
C m
Vector directed
from negative to
positive charge
Charge density:
linear
l
[L–1 TA]
C m–1
Charge/length
surface
s
[L–2 TA]
C m–2
Charge/area
volume
r
[L–3 TA]
C m–3
Charge/volume
POINTS TO PONDER
1 You might wonder why the protons, all carrying positive charges,
are compactly residing inside the nucleus Why do they not fly away |
1 | 1214-1217 | DS
Dipole moment
p
[LTA]
C m
Vector directed
from negative to
positive charge
Charge density:
linear
l
[L–1 TA]
C m–1
Charge/length
surface
s
[L–2 TA]
C m–2
Charge/area
volume
r
[L–3 TA]
C m–3
Charge/volume
POINTS TO PONDER
1 You might wonder why the protons, all carrying positive charges,
are compactly residing inside the nucleus Why do they not fly away You will learn that there is a third kind of a fundamental force,
called the strong force which holds them together |
1 | 1215-1218 | You might wonder why the protons, all carrying positive charges,
are compactly residing inside the nucleus Why do they not fly away You will learn that there is a third kind of a fundamental force,
called the strong force which holds them together The range of
distance where this force is effective is, however, very small ~10-14
m |
1 | 1216-1219 | Why do they not fly away You will learn that there is a third kind of a fundamental force,
called the strong force which holds them together The range of
distance where this force is effective is, however, very small ~10-14
m This is precisely the size of the nucleus |
1 | 1217-1220 | You will learn that there is a third kind of a fundamental force,
called the strong force which holds them together The range of
distance where this force is effective is, however, very small ~10-14
m This is precisely the size of the nucleus Also the electrons are
not allowed to sit on top of the protons, i |
1 | 1218-1221 | The range of
distance where this force is effective is, however, very small ~10-14
m This is precisely the size of the nucleus Also the electrons are
not allowed to sit on top of the protons, i e |
1 | 1219-1222 | This is precisely the size of the nucleus Also the electrons are
not allowed to sit on top of the protons, i e inside the nucleus,
due to the laws of quantum mechanics |
1 | 1220-1223 | Also the electrons are
not allowed to sit on top of the protons, i e inside the nucleus,
due to the laws of quantum mechanics This gives the atoms their
structure as they exist in nature |
1 | 1221-1224 | e inside the nucleus,
due to the laws of quantum mechanics This gives the atoms their
structure as they exist in nature 2 |
1 | 1222-1225 | inside the nucleus,
due to the laws of quantum mechanics This gives the atoms their
structure as they exist in nature 2 Coulomb force and gravitational force follow the same inverse-square
law |
1 | 1223-1226 | This gives the atoms their
structure as they exist in nature 2 Coulomb force and gravitational force follow the same inverse-square
law But gravitational force has only one sign (always attractive), while
Rationalised 2023-24
Electric Charges
and Fields
41
Coulomb force can be of both signs (attractive and repulsive), allowing
possibility of cancellation of electric forces |
1 | 1224-1227 | 2 Coulomb force and gravitational force follow the same inverse-square
law But gravitational force has only one sign (always attractive), while
Rationalised 2023-24
Electric Charges
and Fields
41
Coulomb force can be of both signs (attractive and repulsive), allowing
possibility of cancellation of electric forces This is how gravity, despite
being a much weaker force, can be a dominating and more pervasive
force in nature |
1 | 1225-1228 | Coulomb force and gravitational force follow the same inverse-square
law But gravitational force has only one sign (always attractive), while
Rationalised 2023-24
Electric Charges
and Fields
41
Coulomb force can be of both signs (attractive and repulsive), allowing
possibility of cancellation of electric forces This is how gravity, despite
being a much weaker force, can be a dominating and more pervasive
force in nature 3 |
1 | 1226-1229 | But gravitational force has only one sign (always attractive), while
Rationalised 2023-24
Electric Charges
and Fields
41
Coulomb force can be of both signs (attractive and repulsive), allowing
possibility of cancellation of electric forces This is how gravity, despite
being a much weaker force, can be a dominating and more pervasive
force in nature 3 The constant of proportionality k in Coulomb’s law is a matter of
choice if the unit of charge is to be defined using Coulomb’s law |
1 | 1227-1230 | This is how gravity, despite
being a much weaker force, can be a dominating and more pervasive
force in nature 3 The constant of proportionality k in Coulomb’s law is a matter of
choice if the unit of charge is to be defined using Coulomb’s law In SI
units, however, what is defined is the unit of current (A) via its magnetic
effect (Ampere’s law) and the unit of charge (coulomb) is simply defined
by (1C = 1 A s) |
1 | 1228-1231 | 3 The constant of proportionality k in Coulomb’s law is a matter of
choice if the unit of charge is to be defined using Coulomb’s law In SI
units, however, what is defined is the unit of current (A) via its magnetic
effect (Ampere’s law) and the unit of charge (coulomb) is simply defined
by (1C = 1 A s) In this case, the value of k is no longer arbitrary; it is
approximately 9 × 109 N m2 C–2 |
1 | 1229-1232 | The constant of proportionality k in Coulomb’s law is a matter of
choice if the unit of charge is to be defined using Coulomb’s law In SI
units, however, what is defined is the unit of current (A) via its magnetic
effect (Ampere’s law) and the unit of charge (coulomb) is simply defined
by (1C = 1 A s) In this case, the value of k is no longer arbitrary; it is
approximately 9 × 109 N m2 C–2 4 |
1 | 1230-1233 | In SI
units, however, what is defined is the unit of current (A) via its magnetic
effect (Ampere’s law) and the unit of charge (coulomb) is simply defined
by (1C = 1 A s) In this case, the value of k is no longer arbitrary; it is
approximately 9 × 109 N m2 C–2 4 The rather large value of k, i |
1 | 1231-1234 | In this case, the value of k is no longer arbitrary; it is
approximately 9 × 109 N m2 C–2 4 The rather large value of k, i e |
1 | 1232-1235 | 4 The rather large value of k, i e , the large size of the unit of charge
(1C) from the point of view of electric effects arises because (as
mentioned in point 3 already) the unit of charge is defined in terms of
magnetic forces (forces on current–carrying wires) which are generally
much weaker than the electric forces |
1 | 1233-1236 | The rather large value of k, i e , the large size of the unit of charge
(1C) from the point of view of electric effects arises because (as
mentioned in point 3 already) the unit of charge is defined in terms of
magnetic forces (forces on current–carrying wires) which are generally
much weaker than the electric forces Thus while 1 ampere is a unit
of reasonable size for magnetic effects, 1 C = 1 A s, is too big a unit for
electric effects |
1 | 1234-1237 | e , the large size of the unit of charge
(1C) from the point of view of electric effects arises because (as
mentioned in point 3 already) the unit of charge is defined in terms of
magnetic forces (forces on current–carrying wires) which are generally
much weaker than the electric forces Thus while 1 ampere is a unit
of reasonable size for magnetic effects, 1 C = 1 A s, is too big a unit for
electric effects 5 |
1 | 1235-1238 | , the large size of the unit of charge
(1C) from the point of view of electric effects arises because (as
mentioned in point 3 already) the unit of charge is defined in terms of
magnetic forces (forces on current–carrying wires) which are generally
much weaker than the electric forces Thus while 1 ampere is a unit
of reasonable size for magnetic effects, 1 C = 1 A s, is too big a unit for
electric effects 5 The additive property of charge is not an ‘obvious’ property |
1 | 1236-1239 | Thus while 1 ampere is a unit
of reasonable size for magnetic effects, 1 C = 1 A s, is too big a unit for
electric effects 5 The additive property of charge is not an ‘obvious’ property It is related
to the fact that electric charge has no direction associated with it;
charge is a scalar |
1 | 1237-1240 | 5 The additive property of charge is not an ‘obvious’ property It is related
to the fact that electric charge has no direction associated with it;
charge is a scalar 6 |
1 | 1238-1241 | The additive property of charge is not an ‘obvious’ property It is related
to the fact that electric charge has no direction associated with it;
charge is a scalar 6 Charge is not only a scalar (or invariant) under rotation; it is also
invariant for frames of reference in relative motion |
1 | 1239-1242 | It is related
to the fact that electric charge has no direction associated with it;
charge is a scalar 6 Charge is not only a scalar (or invariant) under rotation; it is also
invariant for frames of reference in relative motion This is not always
true for every scalar |
1 | 1240-1243 | 6 Charge is not only a scalar (or invariant) under rotation; it is also
invariant for frames of reference in relative motion This is not always
true for every scalar For example, kinetic energy is a scalar under
rotation, but is not invariant for frames of reference in relative
motion |
1 | 1241-1244 | Charge is not only a scalar (or invariant) under rotation; it is also
invariant for frames of reference in relative motion This is not always
true for every scalar For example, kinetic energy is a scalar under
rotation, but is not invariant for frames of reference in relative
motion 7 |
1 | 1242-1245 | This is not always
true for every scalar For example, kinetic energy is a scalar under
rotation, but is not invariant for frames of reference in relative
motion 7 Conservation of total charge of an isolated system is a property
independent of the scalar nature of charge noted in point 6 |
1 | 1243-1246 | For example, kinetic energy is a scalar under
rotation, but is not invariant for frames of reference in relative
motion 7 Conservation of total charge of an isolated system is a property
independent of the scalar nature of charge noted in point 6 Conservation refers to invariance in time in a given frame of reference |
1 | 1244-1247 | 7 Conservation of total charge of an isolated system is a property
independent of the scalar nature of charge noted in point 6 Conservation refers to invariance in time in a given frame of reference A quantity may be scalar but not conserved (like kinetic energy in an
inelastic collision) |
1 | 1245-1248 | Conservation of total charge of an isolated system is a property
independent of the scalar nature of charge noted in point 6 Conservation refers to invariance in time in a given frame of reference A quantity may be scalar but not conserved (like kinetic energy in an
inelastic collision) On the other hand, one can have conserved vector
quantity (e |
1 | 1246-1249 | Conservation refers to invariance in time in a given frame of reference A quantity may be scalar but not conserved (like kinetic energy in an
inelastic collision) On the other hand, one can have conserved vector
quantity (e g |
1 | 1247-1250 | A quantity may be scalar but not conserved (like kinetic energy in an
inelastic collision) On the other hand, one can have conserved vector
quantity (e g , angular momentum of an isolated system) |
1 | 1248-1251 | On the other hand, one can have conserved vector
quantity (e g , angular momentum of an isolated system) 8 |
1 | 1249-1252 | g , angular momentum of an isolated system) 8 Quantisation of electric charge is a basic (unexplained) law of nature;
interestingly, there is no analogous law on quantisation of mass |
1 | 1250-1253 | , angular momentum of an isolated system) 8 Quantisation of electric charge is a basic (unexplained) law of nature;
interestingly, there is no analogous law on quantisation of mass 9 |
1 | 1251-1254 | 8 Quantisation of electric charge is a basic (unexplained) law of nature;
interestingly, there is no analogous law on quantisation of mass 9 Superposition principle should not be regarded as ‘obvious’, or
equated with the law of addition of vectors |
1 | 1252-1255 | Quantisation of electric charge is a basic (unexplained) law of nature;
interestingly, there is no analogous law on quantisation of mass 9 Superposition principle should not be regarded as ‘obvious’, or
equated with the law of addition of vectors It says two things:
force on one charge due to another charge is unaffected by the
presence of other charges, and there are no additional three-body,
four-body, etc |
1 | 1253-1256 | 9 Superposition principle should not be regarded as ‘obvious’, or
equated with the law of addition of vectors It says two things:
force on one charge due to another charge is unaffected by the
presence of other charges, and there are no additional three-body,
four-body, etc , forces which arise only when there are more than
two charges |
1 | 1254-1257 | Superposition principle should not be regarded as ‘obvious’, or
equated with the law of addition of vectors It says two things:
force on one charge due to another charge is unaffected by the
presence of other charges, and there are no additional three-body,
four-body, etc , forces which arise only when there are more than
two charges 10 |
1 | 1255-1258 | It says two things:
force on one charge due to another charge is unaffected by the
presence of other charges, and there are no additional three-body,
four-body, etc , forces which arise only when there are more than
two charges 10 The electric field due to a discrete charge configuration is not defined
at the locations of the discrete charges |
1 | 1256-1259 | , forces which arise only when there are more than
two charges 10 The electric field due to a discrete charge configuration is not defined
at the locations of the discrete charges For continuous volume
charge distribution, it is defined at any point in the distribution |
1 | 1257-1260 | 10 The electric field due to a discrete charge configuration is not defined
at the locations of the discrete charges For continuous volume
charge distribution, it is defined at any point in the distribution For a surface charge distribution, electric field is discontinuous
across the surface |
1 | 1258-1261 | The electric field due to a discrete charge configuration is not defined
at the locations of the discrete charges For continuous volume
charge distribution, it is defined at any point in the distribution For a surface charge distribution, electric field is discontinuous
across the surface 11 |
1 | 1259-1262 | For continuous volume
charge distribution, it is defined at any point in the distribution For a surface charge distribution, electric field is discontinuous
across the surface 11 The electric field due to a charge configuration with total charge zero
is not zero; but for distances large compared to the size of
the configuration, its field falls off faster than 1/r 2, typical of field
due to a single charge |
1 | 1260-1263 | For a surface charge distribution, electric field is discontinuous
across the surface 11 The electric field due to a charge configuration with total charge zero
is not zero; but for distances large compared to the size of
the configuration, its field falls off faster than 1/r 2, typical of field
due to a single charge An electric dipole is the simplest example of
this fact |
1 | 1261-1264 | 11 The electric field due to a charge configuration with total charge zero
is not zero; but for distances large compared to the size of
the configuration, its field falls off faster than 1/r 2, typical of field
due to a single charge An electric dipole is the simplest example of
this fact Rationalised 2023-24
42
Physics
EXERCISES
1 |
1 | 1262-1265 | The electric field due to a charge configuration with total charge zero
is not zero; but for distances large compared to the size of
the configuration, its field falls off faster than 1/r 2, typical of field
due to a single charge An electric dipole is the simplest example of
this fact Rationalised 2023-24
42
Physics
EXERCISES
1 1
What is the force between two small charged spheres having
charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air |
1 | 1263-1266 | An electric dipole is the simplest example of
this fact Rationalised 2023-24
42
Physics
EXERCISES
1 1
What is the force between two small charged spheres having
charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air 1 |
1 | 1264-1267 | Rationalised 2023-24
42
Physics
EXERCISES
1 1
What is the force between two small charged spheres having
charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air 1 2
The electrostatic force on a small sphere of charge 0 |
1 | 1265-1268 | 1
What is the force between two small charged spheres having
charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air 1 2
The electrostatic force on a small sphere of charge 0 4 mC due to
another small sphere of charge –0 |
1 | 1266-1269 | 1 2
The electrostatic force on a small sphere of charge 0 4 mC due to
another small sphere of charge –0 8 mC in air is 0 |
1 | 1267-1270 | 2
The electrostatic force on a small sphere of charge 0 4 mC due to
another small sphere of charge –0 8 mC in air is 0 2 N |
1 | 1268-1271 | 4 mC due to
another small sphere of charge –0 8 mC in air is 0 2 N (a) What is
the distance between the two spheres |
1 | 1269-1272 | 8 mC in air is 0 2 N (a) What is
the distance between the two spheres (b) What is the force on the
second sphere due to the first |
1 | 1270-1273 | 2 N (a) What is
the distance between the two spheres (b) What is the force on the
second sphere due to the first 1 |
1 | 1271-1274 | (a) What is
the distance between the two spheres (b) What is the force on the
second sphere due to the first 1 3
Check that the ratio ke2/G memp is dimensionless |
1 | 1272-1275 | (b) What is the force on the
second sphere due to the first 1 3
Check that the ratio ke2/G memp is dimensionless Look up a Table
of Physical Constants and determine the value of this ratio |
1 | 1273-1276 | 1 3
Check that the ratio ke2/G memp is dimensionless Look up a Table
of Physical Constants and determine the value of this ratio What
does the ratio signify |
1 | 1274-1277 | 3
Check that the ratio ke2/G memp is dimensionless Look up a Table
of Physical Constants and determine the value of this ratio What
does the ratio signify 1 |
1 | 1275-1278 | Look up a Table
of Physical Constants and determine the value of this ratio What
does the ratio signify 1 4
(a) Explain the meaning of the statement ‘electric charge of a body
is quantised’ |
1 | 1276-1279 | What
does the ratio signify 1 4
(a) Explain the meaning of the statement ‘electric charge of a body
is quantised’ (b) Why can one ignore quantisation of electric charge when dealing
with macroscopic i |
1 | 1277-1280 | 1 4
(a) Explain the meaning of the statement ‘electric charge of a body
is quantised’ (b) Why can one ignore quantisation of electric charge when dealing
with macroscopic i e |
1 | 1278-1281 | 4
(a) Explain the meaning of the statement ‘electric charge of a body
is quantised’ (b) Why can one ignore quantisation of electric charge when dealing
with macroscopic i e , large scale charges |
1 | 1279-1282 | (b) Why can one ignore quantisation of electric charge when dealing
with macroscopic i e , large scale charges 1 |
1 | 1280-1283 | e , large scale charges 1 5
When a glass rod is rubbed with a silk cloth, charges appear on
both |
1 | 1281-1284 | , large scale charges 1 5
When a glass rod is rubbed with a silk cloth, charges appear on
both A similar phenomenon is observed with many other pairs of
bodies |
1 | 1282-1285 | 1 5
When a glass rod is rubbed with a silk cloth, charges appear on
both A similar phenomenon is observed with many other pairs of
bodies Explain how this observation is consistent with the law of
conservation of charge |
1 | 1283-1286 | 5
When a glass rod is rubbed with a silk cloth, charges appear on
both A similar phenomenon is observed with many other pairs of
bodies Explain how this observation is consistent with the law of
conservation of charge 1 |
1 | 1284-1287 | A similar phenomenon is observed with many other pairs of
bodies Explain how this observation is consistent with the law of
conservation of charge 1 6
Four point charges qA = 2 mC, qB = –5 mC, qC = 2 mC, and qD = –5 mC are
located at the corners of a square ABCD of side 10 cm |
1 | 1285-1288 | Explain how this observation is consistent with the law of
conservation of charge 1 6
Four point charges qA = 2 mC, qB = –5 mC, qC = 2 mC, and qD = –5 mC are
located at the corners of a square ABCD of side 10 cm What is the
force on a charge of 1 mC placed at the centre of the square |
1 | 1286-1289 | 1 6
Four point charges qA = 2 mC, qB = –5 mC, qC = 2 mC, and qD = –5 mC are
located at the corners of a square ABCD of side 10 cm What is the
force on a charge of 1 mC placed at the centre of the square 1 |
1 | 1287-1290 | 6
Four point charges qA = 2 mC, qB = –5 mC, qC = 2 mC, and qD = –5 mC are
located at the corners of a square ABCD of side 10 cm What is the
force on a charge of 1 mC placed at the centre of the square 1 7
(a) An electrostatic field line is a continuous curve |
1 | 1288-1291 | What is the
force on a charge of 1 mC placed at the centre of the square 1 7
(a) An electrostatic field line is a continuous curve That is, a field
line cannot have sudden breaks |
1 | 1289-1292 | 1 7
(a) An electrostatic field line is a continuous curve That is, a field
line cannot have sudden breaks Why not |
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