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1 | 4290-4293 | This is unlike the electric dipole where these field lines
begin from a positive charge and end on the negative charge or escape
to infinity FIGURE 5 1 The
arrangement of iron
filings surrounding a
bar magnet The
pattern mimics
magnetic field lines |
1 | 4291-4294 | FIGURE 5 1 The
arrangement of iron
filings surrounding a
bar magnet The
pattern mimics
magnetic field lines The pattern suggests
that the bar magnet
is a magnetic dipole |
1 | 4292-4295 | 1 The
arrangement of iron
filings surrounding a
bar magnet The
pattern mimics
magnetic field lines The pattern suggests
that the bar magnet
is a magnetic dipole *
In some textbooks the magnetic field lines are called magnetic lines of force |
1 | 4293-4296 | The
pattern mimics
magnetic field lines The pattern suggests
that the bar magnet
is a magnetic dipole *
In some textbooks the magnetic field lines are called magnetic lines of force This nomenclature is avoided since it can be confusing |
1 | 4294-4297 | The pattern suggests
that the bar magnet
is a magnetic dipole *
In some textbooks the magnetic field lines are called magnetic lines of force This nomenclature is avoided since it can be confusing Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge |
1 | 4295-4298 | *
In some textbooks the magnetic field lines are called magnetic lines of force This nomenclature is avoided since it can be confusing Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge Rationalised 2023-24
Physics
138
FIGURE 5 |
1 | 4296-4299 | This nomenclature is avoided since it can be confusing Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge Rationalised 2023-24
Physics
138
FIGURE 5 3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its similarity
to that of a bar magnet |
1 | 4297-4300 | Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge Rationalised 2023-24
Physics
138
FIGURE 5 3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its similarity
to that of a bar magnet (b) A magnetic needle
in a uniform magnetic field B |
1 | 4298-4301 | Rationalised 2023-24
Physics
138
FIGURE 5 3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its similarity
to that of a bar magnet (b) A magnetic needle
in a uniform magnetic field B The
arrangement may be used to
determine either B or the magnetic
moment m of the needle |
1 | 4299-4302 | 3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its similarity
to that of a bar magnet (b) A magnetic needle
in a uniform magnetic field B The
arrangement may be used to
determine either B or the magnetic
moment m of the needle (ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point |
1 | 4300-4303 | (b) A magnetic needle
in a uniform magnetic field B The
arrangement may be used to
determine either B or the magnetic
moment m of the needle (ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point (iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B |
1 | 4301-4304 | The
arrangement may be used to
determine either B or the magnetic
moment m of the needle (ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point (iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B In Fig |
1 | 4302-4305 | (ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point (iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B In Fig 5 |
1 | 4303-4306 | (iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B In Fig 5 2(a), B is larger around region
ii than in region i |
1 | 4304-4307 | In Fig 5 2(a), B is larger around region
ii than in region i (iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection |
1 | 4305-4308 | 5 2(a), B is larger around region
ii than in region i (iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection One can plot the magnetic field lines
in a variety of ways |
1 | 4306-4309 | 2(a), B is larger around region
ii than in region i (iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection One can plot the magnetic field lines
in a variety of ways One way is to place a
small magnetic compass needle at various
positions and note its orientation |
1 | 4307-4310 | (iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection One can plot the magnetic field lines
in a variety of ways One way is to place a
small magnetic compass needle at various
positions and note its orientation This
gives us an idea of the magnetic field
direction at various points in space |
1 | 4308-4311 | One can plot the magnetic field lines
in a variety of ways One way is to place a
small magnetic compass needle at various
positions and note its orientation This
gives us an idea of the magnetic field
direction at various points in space 5 |
1 | 4309-4312 | One way is to place a
small magnetic compass needle at various
positions and note its orientation This
gives us an idea of the magnetic field
direction at various points in space 5 2 |
1 | 4310-4313 | This
gives us an idea of the magnetic field
direction at various points in space 5 2 2 Bar magnet as an equivalent
solenoid
In the previous chapter, we have explained
how a current loop acts as a magnetic
dipole (Section 4 |
1 | 4311-4314 | 5 2 2 Bar magnet as an equivalent
solenoid
In the previous chapter, we have explained
how a current loop acts as a magnetic
dipole (Section 4 10) |
1 | 4312-4315 | 2 2 Bar magnet as an equivalent
solenoid
In the previous chapter, we have explained
how a current loop acts as a magnetic
dipole (Section 4 10) We mentioned
Ampere’s hypothesis that all magnetic
phenomena can be explained in terms of
circulating currents |
1 | 4313-4316 | 2 Bar magnet as an equivalent
solenoid
In the previous chapter, we have explained
how a current loop acts as a magnetic
dipole (Section 4 10) We mentioned
Ampere’s hypothesis that all magnetic
phenomena can be explained in terms of
circulating currents FIGURE 5 |
1 | 4314-4317 | 10) We mentioned
Ampere’s hypothesis that all magnetic
phenomena can be explained in terms of
circulating currents FIGURE 5 2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole |
1 | 4315-4318 | We mentioned
Ampere’s hypothesis that all magnetic
phenomena can be explained in terms of
circulating currents FIGURE 5 2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole At large distances, the field lines are very similar |
1 | 4316-4319 | FIGURE 5 2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole At large distances, the field lines are very similar The curves
labelled i and ii are closed Gaussian surfaces |
1 | 4317-4320 | 2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole At large distances, the field lines are very similar The curves
labelled i and ii are closed Gaussian surfaces Rationalised 2023-24
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid |
1 | 4318-4321 | At large distances, the field lines are very similar The curves
labelled i and ii are closed Gaussian surfaces Rationalised 2023-24
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid Cutting a bar magnet in
half is like cutting a solenoid |
1 | 4319-4322 | The curves
labelled i and ii are closed Gaussian surfaces Rationalised 2023-24
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid Cutting a bar magnet in
half is like cutting a solenoid We get two smaller solenoids with weaker
magnetic properties |
1 | 4320-4323 | Rationalised 2023-24
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid Cutting a bar magnet in
half is like cutting a solenoid We get two smaller solenoids with weaker
magnetic properties The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face |
1 | 4321-4324 | Cutting a bar magnet in
half is like cutting a solenoid We get two smaller solenoids with weaker
magnetic properties The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases |
1 | 4322-4325 | We get two smaller solenoids with weaker
magnetic properties The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases To make this analogy more firm we calculate the axial field of a finite
solenoid depicted in Fig |
1 | 4323-4326 | The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases To make this analogy more firm we calculate the axial field of a finite
solenoid depicted in Fig 5 |
1 | 4324-4327 | One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases To make this analogy more firm we calculate the axial field of a finite
solenoid depicted in Fig 5 3 (a) |
1 | 4325-4328 | To make this analogy more firm we calculate the axial field of a finite
solenoid depicted in Fig 5 3 (a) We shall demonstrate that at large
distances this axial field resembles that of a bar magnet |
1 | 4326-4329 | 5 3 (a) We shall demonstrate that at large
distances this axial field resembles that of a bar magnet 0
3
2
4
m
B
r
µ
π
=
(5 |
1 | 4327-4330 | 3 (a) We shall demonstrate that at large
distances this axial field resembles that of a bar magnet 0
3
2
4
m
B
r
µ
π
=
(5 1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally |
1 | 4328-4331 | We shall demonstrate that at large
distances this axial field resembles that of a bar magnet 0
3
2
4
m
B
r
µ
π
=
(5 1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally Thus, a bar magnet and a solenoid produce similar
magnetic fields |
1 | 4329-4332 | 0
3
2
4
m
B
r
µ
π
=
(5 1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally Thus, a bar magnet and a solenoid produce similar
magnetic fields The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field |
1 | 4330-4333 | 1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally Thus, a bar magnet and a solenoid produce similar
magnetic fields The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field 5 |
1 | 4331-4334 | Thus, a bar magnet and a solenoid produce similar
magnetic fields The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field 5 2 |
1 | 4332-4335 | The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field 5 2 3 The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m and
allowing it to oscillate in the magnetic field |
1 | 4333-4336 | 5 2 3 The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m and
allowing it to oscillate in the magnetic field This arrangement is shown in
Fig |
1 | 4334-4337 | 2 3 The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m and
allowing it to oscillate in the magnetic field This arrangement is shown in
Fig 5 |
1 | 4335-4338 | 3 The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m and
allowing it to oscillate in the magnetic field This arrangement is shown in
Fig 5 3(b) |
1 | 4336-4339 | This arrangement is shown in
Fig 5 3(b) The torque on the needle is [see Eq |
1 | 4337-4340 | 5 3(b) The torque on the needle is [see Eq (4 |
1 | 4338-4341 | 3(b) The torque on the needle is [see Eq (4 23)],
ttttt = m × B
(5 |
1 | 4339-4342 | The torque on the needle is [see Eq (4 23)],
ttttt = m × B
(5 2)
In magnitude t = mB sinq
Here ttttt is restoring torque and q is the angle between m and B |
1 | 4340-4343 | (4 23)],
ttttt = m × B
(5 2)
In magnitude t = mB sinq
Here ttttt is restoring torque and q is the angle between m and B An expression for magnetic potential energy can also be obtained on
lines similar to electrostatic potential energy |
1 | 4341-4344 | 23)],
ttttt = m × B
(5 2)
In magnitude t = mB sinq
Here ttttt is restoring torque and q is the angle between m and B An expression for magnetic potential energy can also be obtained on
lines similar to electrostatic potential energy The magnetic potential energy Um is given by
U
m = ∫τ θd
θ
( )
=
= −
∫mB
d
mB
sin
cos
θ
θ
θ
= –m |
1 | 4342-4345 | 2)
In magnitude t = mB sinq
Here ttttt is restoring torque and q is the angle between m and B An expression for magnetic potential energy can also be obtained on
lines similar to electrostatic potential energy The magnetic potential energy Um is given by
U
m = ∫τ θd
θ
( )
=
= −
∫mB
d
mB
sin
cos
θ
θ
θ
= –m B
(5 |
1 | 4343-4346 | An expression for magnetic potential energy can also be obtained on
lines similar to electrostatic potential energy The magnetic potential energy Um is given by
U
m = ∫τ θd
θ
( )
=
= −
∫mB
d
mB
sin
cos
θ
θ
θ
= –m B
(5 3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience |
1 | 4344-4347 | The magnetic potential energy Um is given by
U
m = ∫τ θd
θ
( )
=
= −
∫mB
d
mB
sin
cos
θ
θ
θ
= –m B
(5 3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience Taking the constant of integration to be
zero means fixing the zero of potential energy at q = 90°, i |
1 | 4345-4348 | B
(5 3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience Taking the constant of integration to be
zero means fixing the zero of potential energy at q = 90°, i e |
1 | 4346-4349 | 3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience Taking the constant of integration to be
zero means fixing the zero of potential energy at q = 90°, i e , when the
needle is perpendicular to the field |
1 | 4347-4350 | Taking the constant of integration to be
zero means fixing the zero of potential energy at q = 90°, i e , when the
needle is perpendicular to the field Equation (5 |
1 | 4348-4351 | e , when the
needle is perpendicular to the field Equation (5 6) shows that potential
energy is minimum (= –mB) at q = 0° (most stable position) and maximum
(= +mB) at q = 180° (most unstable position) |
1 | 4349-4352 | , when the
needle is perpendicular to the field Equation (5 6) shows that potential
energy is minimum (= –mB) at q = 0° (most stable position) and maximum
(= +mB) at q = 180° (most unstable position) Example 5 |
1 | 4350-4353 | Equation (5 6) shows that potential
energy is minimum (= –mB) at q = 0° (most stable position) and maximum
(= +mB) at q = 180° (most unstable position) Example 5 1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length |
1 | 4351-4354 | 6) shows that potential
energy is minimum (= –mB) at q = 0° (most stable position) and maximum
(= +mB) at q = 180° (most unstable position) Example 5 1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length (b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force |
1 | 4352-4355 | Example 5 1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length (b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque |
1 | 4353-4356 | 1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length (b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque Why |
1 | 4354-4357 | (b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque Why EXAMPLE 5 |
1 | 4355-4358 | An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque Why EXAMPLE 5 1
Rationalised 2023-24
Physics
140
EXAMPLE 5 |
1 | 4356-4359 | Why EXAMPLE 5 1
Rationalised 2023-24
Physics
140
EXAMPLE 5 1
(c) Must every magnetic configuration have a north pole and a south
pole |
1 | 4357-4360 | EXAMPLE 5 1
Rationalised 2023-24
Physics
140
EXAMPLE 5 1
(c) Must every magnetic configuration have a north pole and a south
pole What about the field due to a toroid |
1 | 4358-4361 | 1
Rationalised 2023-24
Physics
140
EXAMPLE 5 1
(c) Must every magnetic configuration have a north pole and a south
pole What about the field due to a toroid (d) Two identical looking iron bars A and B are given, one of which
is definitely known to be magnetised |
1 | 4359-4362 | 1
(c) Must every magnetic configuration have a north pole and a south
pole What about the field due to a toroid (d) Two identical looking iron bars A and B are given, one of which
is definitely known to be magnetised (We do not know which
one |
1 | 4360-4363 | What about the field due to a toroid (d) Two identical looking iron bars A and B are given, one of which
is definitely known to be magnetised (We do not know which
one ) How would one ascertain whether or not both are
magnetised |
1 | 4361-4364 | (d) Two identical looking iron bars A and B are given, one of which
is definitely known to be magnetised (We do not know which
one ) How would one ascertain whether or not both are
magnetised If only one is magnetised, how does one ascertain
which one |
1 | 4362-4365 | (We do not know which
one ) How would one ascertain whether or not both are
magnetised If only one is magnetised, how does one ascertain
which one [Use nothing else but the bars A and B |
1 | 4363-4366 | ) How would one ascertain whether or not both are
magnetised If only one is magnetised, how does one ascertain
which one [Use nothing else but the bars A and B ]
Solution
(a) In either case, one gets two magnets, each with a north and
south pole |
1 | 4364-4367 | If only one is magnetised, how does one ascertain
which one [Use nothing else but the bars A and B ]
Solution
(a) In either case, one gets two magnets, each with a north and
south pole (b) No force if the field is uniform |
1 | 4365-4368 | [Use nothing else but the bars A and B ]
Solution
(a) In either case, one gets two magnets, each with a north and
south pole (b) No force if the field is uniform The iron nail experiences a non-
uniform field due to the bar magnet |
1 | 4366-4369 | ]
Solution
(a) In either case, one gets two magnets, each with a north and
south pole (b) No force if the field is uniform The iron nail experiences a non-
uniform field due to the bar magnet There is induced magnetic
moment in the nail, therefore, it experiences both force and
torque |
1 | 4367-4370 | (b) No force if the field is uniform The iron nail experiences a non-
uniform field due to the bar magnet There is induced magnetic
moment in the nail, therefore, it experiences both force and
torque The net force is attractive because the induced south
pole (say) in the nail is closer to the north pole of magnet than
induced north pole |
1 | 4368-4371 | The iron nail experiences a non-
uniform field due to the bar magnet There is induced magnetic
moment in the nail, therefore, it experiences both force and
torque The net force is attractive because the induced south
pole (say) in the nail is closer to the north pole of magnet than
induced north pole (c) Not necessarily |
1 | 4369-4372 | There is induced magnetic
moment in the nail, therefore, it experiences both force and
torque The net force is attractive because the induced south
pole (say) in the nail is closer to the north pole of magnet than
induced north pole (c) Not necessarily True only if the source of the field has a net
non-zero magnetic moment |
1 | 4370-4373 | The net force is attractive because the induced south
pole (say) in the nail is closer to the north pole of magnet than
induced north pole (c) Not necessarily True only if the source of the field has a net
non-zero magnetic moment This is not so for a toroid or even for
a straight infinite conductor |
1 | 4371-4374 | (c) Not necessarily True only if the source of the field has a net
non-zero magnetic moment This is not so for a toroid or even for
a straight infinite conductor (d) Try to bring different ends of the bars closer |
1 | 4372-4375 | True only if the source of the field has a net
non-zero magnetic moment This is not so for a toroid or even for
a straight infinite conductor (d) Try to bring different ends of the bars closer A repulsive force in
some situation establishes that both are magnetised |
1 | 4373-4376 | This is not so for a toroid or even for
a straight infinite conductor (d) Try to bring different ends of the bars closer A repulsive force in
some situation establishes that both are magnetised If it is
always attractive, then one of them is not magnetised |
1 | 4374-4377 | (d) Try to bring different ends of the bars closer A repulsive force in
some situation establishes that both are magnetised If it is
always attractive, then one of them is not magnetised In a bar
magnet the intensity of the magnetic field is the strongest at the
two ends (poles) and weakest at the central region |
1 | 4375-4378 | A repulsive force in
some situation establishes that both are magnetised If it is
always attractive, then one of them is not magnetised In a bar
magnet the intensity of the magnetic field is the strongest at the
two ends (poles) and weakest at the central region This fact
may be used to determine whether A or B is the magnet |
1 | 4376-4379 | If it is
always attractive, then one of them is not magnetised In a bar
magnet the intensity of the magnetic field is the strongest at the
two ends (poles) and weakest at the central region This fact
may be used to determine whether A or B is the magnet In this
case, to see which one of the two bars is a magnet, pick up one,
(say, A) and lower one of its ends; first on one of the ends of the
other (say, B), and then on the middle of B |
1 | 4377-4380 | In a bar
magnet the intensity of the magnetic field is the strongest at the
two ends (poles) and weakest at the central region This fact
may be used to determine whether A or B is the magnet In this
case, to see which one of the two bars is a magnet, pick up one,
(say, A) and lower one of its ends; first on one of the ends of the
other (say, B), and then on the middle of B If you notice that in
the middle of B, A experiences no force, then B is magnetised |
1 | 4378-4381 | This fact
may be used to determine whether A or B is the magnet In this
case, to see which one of the two bars is a magnet, pick up one,
(say, A) and lower one of its ends; first on one of the ends of the
other (say, B), and then on the middle of B If you notice that in
the middle of B, A experiences no force, then B is magnetised If
you do not notice any change from the end to the middle of B,
then A is magnetised |
1 | 4379-4382 | In this
case, to see which one of the two bars is a magnet, pick up one,
(say, A) and lower one of its ends; first on one of the ends of the
other (say, B), and then on the middle of B If you notice that in
the middle of B, A experiences no force, then B is magnetised If
you do not notice any change from the end to the middle of B,
then A is magnetised 5 |
1 | 4380-4383 | If you notice that in
the middle of B, A experiences no force, then B is magnetised If
you do not notice any change from the end to the middle of B,
then A is magnetised 5 2 |
1 | 4381-4384 | If
you do not notice any change from the end to the middle of B,
then A is magnetised 5 2 4 The electrostatic analog
Comparison of Eqs |
1 | 4382-4385 | 5 2 4 The electrostatic analog
Comparison of Eqs (5 |
1 | 4383-4386 | 2 4 The electrostatic analog
Comparison of Eqs (5 2), (5 |
1 | 4384-4387 | 4 The electrostatic analog
Comparison of Eqs (5 2), (5 3) and (5 |
1 | 4385-4388 | (5 2), (5 3) and (5 6) with the corresponding equations
for electric dipole (Chapter 1), suggests that magnetic field at large
distances due to a bar magnet of magnetic moment m can be obtained
from the equation for electric field due to an electric dipole of dipole moment
p, by making the following replacements:
E→
B , p
m
→
,
0
0
1
4
4
µ
ε
→
π
π
In particular, we can write down the equatorial field (BE) of a bar magnet
at a distance r, for r >> l, where l is the size of the magnet:
0
3
4
E
r
= −µ
π
m
B
(5 |
1 | 4386-4389 | 2), (5 3) and (5 6) with the corresponding equations
for electric dipole (Chapter 1), suggests that magnetic field at large
distances due to a bar magnet of magnetic moment m can be obtained
from the equation for electric field due to an electric dipole of dipole moment
p, by making the following replacements:
E→
B , p
m
→
,
0
0
1
4
4
µ
ε
→
π
π
In particular, we can write down the equatorial field (BE) of a bar magnet
at a distance r, for r >> l, where l is the size of the magnet:
0
3
4
E
r
= −µ
π
m
B
(5 4)
Likewise, the axial field (BA) of a bar magnet for r >> l is:
0
3
2
4
A
r
=µ
π
m
B
(5 |
1 | 4387-4390 | 3) and (5 6) with the corresponding equations
for electric dipole (Chapter 1), suggests that magnetic field at large
distances due to a bar magnet of magnetic moment m can be obtained
from the equation for electric field due to an electric dipole of dipole moment
p, by making the following replacements:
E→
B , p
m
→
,
0
0
1
4
4
µ
ε
→
π
π
In particular, we can write down the equatorial field (BE) of a bar magnet
at a distance r, for r >> l, where l is the size of the magnet:
0
3
4
E
r
= −µ
π
m
B
(5 4)
Likewise, the axial field (BA) of a bar magnet for r >> l is:
0
3
2
4
A
r
=µ
π
m
B
(5 5)
Rationalised 2023-24
141
Magnetism and
Matter
Equation (5 |
1 | 4388-4391 | 6) with the corresponding equations
for electric dipole (Chapter 1), suggests that magnetic field at large
distances due to a bar magnet of magnetic moment m can be obtained
from the equation for electric field due to an electric dipole of dipole moment
p, by making the following replacements:
E→
B , p
m
→
,
0
0
1
4
4
µ
ε
→
π
π
In particular, we can write down the equatorial field (BE) of a bar magnet
at a distance r, for r >> l, where l is the size of the magnet:
0
3
4
E
r
= −µ
π
m
B
(5 4)
Likewise, the axial field (BA) of a bar magnet for r >> l is:
0
3
2
4
A
r
=µ
π
m
B
(5 5)
Rationalised 2023-24
141
Magnetism and
Matter
Equation (5 8) is just Eq |
1 | 4389-4392 | 4)
Likewise, the axial field (BA) of a bar magnet for r >> l is:
0
3
2
4
A
r
=µ
π
m
B
(5 5)
Rationalised 2023-24
141
Magnetism and
Matter
Equation (5 8) is just Eq (5 |
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