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1 | 3290-3293 | The wire is perpendicular to the plane of the paper A ring of
compass needles surrounds the wire The orientation of the needles is
shown when (a) the current emerges out of the plane of the paper,
(b) the current moves into the plane of the paper (c) The arrangement of
iron filings around the wire |
1 | 3291-3294 | A ring of
compass needles surrounds the wire The orientation of the needles is
shown when (a) the current emerges out of the plane of the paper,
(b) the current moves into the plane of the paper (c) The arrangement of
iron filings around the wire The darkened ends of the needle represent
north poles |
1 | 3292-3295 | The orientation of the needles is
shown when (a) the current emerges out of the plane of the paper,
(b) the current moves into the plane of the paper (c) The arrangement of
iron filings around the wire The darkened ends of the needle represent
north poles The effect of the earth’s magnetic field is neglected |
1 | 3293-3296 | (c) The arrangement of
iron filings around the wire The darkened ends of the needle represent
north poles The effect of the earth’s magnetic field is neglected *
A dot appears like the tip of an arrow pointed at you, a cross is like the feathered
tail of an arrow moving away from you |
1 | 3294-3297 | The darkened ends of the needle represent
north poles The effect of the earth’s magnetic field is neglected *
A dot appears like the tip of an arrow pointed at you, a cross is like the feathered
tail of an arrow moving away from you Hans Christian Oersted
(1777–1851)
Danish
physicist and chemist,
professor at Copenhagen |
1 | 3295-3298 | The effect of the earth’s magnetic field is neglected *
A dot appears like the tip of an arrow pointed at you, a cross is like the feathered
tail of an arrow moving away from you Hans Christian Oersted
(1777–1851)
Danish
physicist and chemist,
professor at Copenhagen He
observed
that
compass needle suffers aa
deflection when placed
near a wire carrying an
electric
current |
1 | 3296-3299 | *
A dot appears like the tip of an arrow pointed at you, a cross is like the feathered
tail of an arrow moving away from you Hans Christian Oersted
(1777–1851)
Danish
physicist and chemist,
professor at Copenhagen He
observed
that
compass needle suffers aa
deflection when placed
near a wire carrying an
electric
current This
discovery gave the first
empirical evidence of a
connection between electric
and magnetic phenomena |
1 | 3297-3300 | Hans Christian Oersted
(1777–1851)
Danish
physicist and chemist,
professor at Copenhagen He
observed
that
compass needle suffers aa
deflection when placed
near a wire carrying an
electric
current This
discovery gave the first
empirical evidence of a
connection between electric
and magnetic phenomena HANS CHRISTIAN OERSTED (1777–1851)
Rationalised 2023-24
109
Moving Charges and
Magnetism
E = Q ˆr / (4pe0)r2
(4 |
1 | 3298-3301 | He
observed
that
compass needle suffers aa
deflection when placed
near a wire carrying an
electric
current This
discovery gave the first
empirical evidence of a
connection between electric
and magnetic phenomena HANS CHRISTIAN OERSTED (1777–1851)
Rationalised 2023-24
109
Moving Charges and
Magnetism
E = Q ˆr / (4pe0)r2
(4 1)
where ˆr is unit vector along r, and the field E is a vector
field |
1 | 3299-3302 | This
discovery gave the first
empirical evidence of a
connection between electric
and magnetic phenomena HANS CHRISTIAN OERSTED (1777–1851)
Rationalised 2023-24
109
Moving Charges and
Magnetism
E = Q ˆr / (4pe0)r2
(4 1)
where ˆr is unit vector along r, and the field E is a vector
field A charge q interacts with this field and experiences
a force F given by
F = q E = q Q ˆr / (4pe0) r 2
(4 |
1 | 3300-3303 | HANS CHRISTIAN OERSTED (1777–1851)
Rationalised 2023-24
109
Moving Charges and
Magnetism
E = Q ˆr / (4pe0)r2
(4 1)
where ˆr is unit vector along r, and the field E is a vector
field A charge q interacts with this field and experiences
a force F given by
F = q E = q Q ˆr / (4pe0) r 2
(4 2)
As pointed out in the Chapter 1, the field E is not just
an artefact but has a physical role |
1 | 3301-3304 | 1)
where ˆr is unit vector along r, and the field E is a vector
field A charge q interacts with this field and experiences
a force F given by
F = q E = q Q ˆr / (4pe0) r 2
(4 2)
As pointed out in the Chapter 1, the field E is not just
an artefact but has a physical role It can convey energy
and momentum and is not established instantaneously
but takes finite time to propagate |
1 | 3302-3305 | A charge q interacts with this field and experiences
a force F given by
F = q E = q Q ˆr / (4pe0) r 2
(4 2)
As pointed out in the Chapter 1, the field E is not just
an artefact but has a physical role It can convey energy
and momentum and is not established instantaneously
but takes finite time to propagate The concept of a field
was specially stressed by Faraday and was incorporated
by Maxwell in his unification of electricity and magnetism |
1 | 3303-3306 | 2)
As pointed out in the Chapter 1, the field E is not just
an artefact but has a physical role It can convey energy
and momentum and is not established instantaneously
but takes finite time to propagate The concept of a field
was specially stressed by Faraday and was incorporated
by Maxwell in his unification of electricity and magnetism In addition to depending on each point in space, it can
also vary with time, i |
1 | 3304-3307 | It can convey energy
and momentum and is not established instantaneously
but takes finite time to propagate The concept of a field
was specially stressed by Faraday and was incorporated
by Maxwell in his unification of electricity and magnetism In addition to depending on each point in space, it can
also vary with time, i e |
1 | 3305-3308 | The concept of a field
was specially stressed by Faraday and was incorporated
by Maxwell in his unification of electricity and magnetism In addition to depending on each point in space, it can
also vary with time, i e , be a function of time |
1 | 3306-3309 | In addition to depending on each point in space, it can
also vary with time, i e , be a function of time In our
discussions in this chapter, we will assume that the fields
do not change with time |
1 | 3307-3310 | e , be a function of time In our
discussions in this chapter, we will assume that the fields
do not change with time The field at a particular point can be due to one or
more charges |
1 | 3308-3311 | , be a function of time In our
discussions in this chapter, we will assume that the fields
do not change with time The field at a particular point can be due to one or
more charges If there are more charges the fields add
vectorially |
1 | 3309-3312 | In our
discussions in this chapter, we will assume that the fields
do not change with time The field at a particular point can be due to one or
more charges If there are more charges the fields add
vectorially You have already learnt in Chapter 1 that this
is called the principle of superposition |
1 | 3310-3313 | The field at a particular point can be due to one or
more charges If there are more charges the fields add
vectorially You have already learnt in Chapter 1 that this
is called the principle of superposition Once the field is
known, the force on a test charge is given by Eq |
1 | 3311-3314 | If there are more charges the fields add
vectorially You have already learnt in Chapter 1 that this
is called the principle of superposition Once the field is
known, the force on a test charge is given by Eq (4 |
1 | 3312-3315 | You have already learnt in Chapter 1 that this
is called the principle of superposition Once the field is
known, the force on a test charge is given by Eq (4 2) |
1 | 3313-3316 | Once the field is
known, the force on a test charge is given by Eq (4 2) Just as static charges produce an electric field, the
currents or moving charges produce (in addition) a
magnetic field, denoted by B (r), again a vector field |
1 | 3314-3317 | (4 2) Just as static charges produce an electric field, the
currents or moving charges produce (in addition) a
magnetic field, denoted by B (r), again a vector field It
has several basic properties identical to the electric field |
1 | 3315-3318 | 2) Just as static charges produce an electric field, the
currents or moving charges produce (in addition) a
magnetic field, denoted by B (r), again a vector field It
has several basic properties identical to the electric field It is defined at each point in space (and can in addition
depend on time) |
1 | 3316-3319 | Just as static charges produce an electric field, the
currents or moving charges produce (in addition) a
magnetic field, denoted by B (r), again a vector field It
has several basic properties identical to the electric field It is defined at each point in space (and can in addition
depend on time) Experimentally, it is found to obey the
principle of superposition: the magnetic field of several
sources is the vector addition of magnetic field of each
individual source |
1 | 3317-3320 | It
has several basic properties identical to the electric field It is defined at each point in space (and can in addition
depend on time) Experimentally, it is found to obey the
principle of superposition: the magnetic field of several
sources is the vector addition of magnetic field of each
individual source 4 |
1 | 3318-3321 | It is defined at each point in space (and can in addition
depend on time) Experimentally, it is found to obey the
principle of superposition: the magnetic field of several
sources is the vector addition of magnetic field of each
individual source 4 2 |
1 | 3319-3322 | Experimentally, it is found to obey the
principle of superposition: the magnetic field of several
sources is the vector addition of magnetic field of each
individual source 4 2 2 Magnetic Field, Lorentz Force
Let us suppose that there is a point charge q (moving
with a velocity v and, located at r at a given time t) in
presence of both the electric field E (r) and the magnetic
field B (r) |
1 | 3320-3323 | 4 2 2 Magnetic Field, Lorentz Force
Let us suppose that there is a point charge q (moving
with a velocity v and, located at r at a given time t) in
presence of both the electric field E (r) and the magnetic
field B (r) The force on an electric charge q due to both
of them can be written as
F = q [ E (r) + v × B (r)] º Felectric +Fmagnetic
(4 |
1 | 3321-3324 | 2 2 Magnetic Field, Lorentz Force
Let us suppose that there is a point charge q (moving
with a velocity v and, located at r at a given time t) in
presence of both the electric field E (r) and the magnetic
field B (r) The force on an electric charge q due to both
of them can be written as
F = q [ E (r) + v × B (r)] º Felectric +Fmagnetic
(4 3)
This force was given first by H |
1 | 3322-3325 | 2 Magnetic Field, Lorentz Force
Let us suppose that there is a point charge q (moving
with a velocity v and, located at r at a given time t) in
presence of both the electric field E (r) and the magnetic
field B (r) The force on an electric charge q due to both
of them can be written as
F = q [ E (r) + v × B (r)] º Felectric +Fmagnetic
(4 3)
This force was given first by H A |
1 | 3323-3326 | The force on an electric charge q due to both
of them can be written as
F = q [ E (r) + v × B (r)] º Felectric +Fmagnetic
(4 3)
This force was given first by H A Lorentz based on the extensive
experiments of Ampere and others |
1 | 3324-3327 | 3)
This force was given first by H A Lorentz based on the extensive
experiments of Ampere and others It is called the Lorentz force |
1 | 3325-3328 | A Lorentz based on the extensive
experiments of Ampere and others It is called the Lorentz force You
have already studied in detail the force due to the electric field |
1 | 3326-3329 | Lorentz based on the extensive
experiments of Ampere and others It is called the Lorentz force You
have already studied in detail the force due to the electric field If we
look at the interaction with the magnetic field, we find the following
features |
1 | 3327-3330 | It is called the Lorentz force You
have already studied in detail the force due to the electric field If we
look at the interaction with the magnetic field, we find the following
features (i)
It depends on q, v and B (charge of the particle, the velocity and the
magnetic field) |
1 | 3328-3331 | You
have already studied in detail the force due to the electric field If we
look at the interaction with the magnetic field, we find the following
features (i)
It depends on q, v and B (charge of the particle, the velocity and the
magnetic field) Force on a negative charge is opposite to that on a
positive charge |
1 | 3329-3332 | If we
look at the interaction with the magnetic field, we find the following
features (i)
It depends on q, v and B (charge of the particle, the velocity and the
magnetic field) Force on a negative charge is opposite to that on a
positive charge (ii) The magnetic force q [ v × B ] includes a vector product of velocity
and magnetic field |
1 | 3330-3333 | (i)
It depends on q, v and B (charge of the particle, the velocity and the
magnetic field) Force on a negative charge is opposite to that on a
positive charge (ii) The magnetic force q [ v × B ] includes a vector product of velocity
and magnetic field The vector product makes the force due to magnetic
HENDRIK ANTOON LORENTZ (1853 – 1928)
Hendrik Antoon Lorentz
(1853 – 1928) Dutch
theoretical
physicist,
professor at Leiden |
1 | 3331-3334 | Force on a negative charge is opposite to that on a
positive charge (ii) The magnetic force q [ v × B ] includes a vector product of velocity
and magnetic field The vector product makes the force due to magnetic
HENDRIK ANTOON LORENTZ (1853 – 1928)
Hendrik Antoon Lorentz
(1853 – 1928) Dutch
theoretical
physicist,
professor at Leiden He
investigated
the
relationship
between
electricity, magnetism, and
mechanics |
1 | 3332-3335 | (ii) The magnetic force q [ v × B ] includes a vector product of velocity
and magnetic field The vector product makes the force due to magnetic
HENDRIK ANTOON LORENTZ (1853 – 1928)
Hendrik Antoon Lorentz
(1853 – 1928) Dutch
theoretical
physicist,
professor at Leiden He
investigated
the
relationship
between
electricity, magnetism, and
mechanics In order to
explain the observed effect
of magnetic fields on
emitters of light (Zeeman
effect), he postulated the
existence of electric charges
in the atom, for which he
was awarded the Nobel Prize
in 1902 |
1 | 3333-3336 | The vector product makes the force due to magnetic
HENDRIK ANTOON LORENTZ (1853 – 1928)
Hendrik Antoon Lorentz
(1853 – 1928) Dutch
theoretical
physicist,
professor at Leiden He
investigated
the
relationship
between
electricity, magnetism, and
mechanics In order to
explain the observed effect
of magnetic fields on
emitters of light (Zeeman
effect), he postulated the
existence of electric charges
in the atom, for which he
was awarded the Nobel Prize
in 1902 He derived a set of
transformation equations
(known
after
him,
as
Lorentz
transformation
equations) by some tangled
mathematical arguments,
but he was not aware that
these equations hinge on a
new concept of space and
time |
1 | 3334-3337 | He
investigated
the
relationship
between
electricity, magnetism, and
mechanics In order to
explain the observed effect
of magnetic fields on
emitters of light (Zeeman
effect), he postulated the
existence of electric charges
in the atom, for which he
was awarded the Nobel Prize
in 1902 He derived a set of
transformation equations
(known
after
him,
as
Lorentz
transformation
equations) by some tangled
mathematical arguments,
but he was not aware that
these equations hinge on a
new concept of space and
time Rationalised 2023-24
Physics
110
field vanish (become zero) if velocity and magnetic field are parallel
or anti-parallel |
1 | 3335-3338 | In order to
explain the observed effect
of magnetic fields on
emitters of light (Zeeman
effect), he postulated the
existence of electric charges
in the atom, for which he
was awarded the Nobel Prize
in 1902 He derived a set of
transformation equations
(known
after
him,
as
Lorentz
transformation
equations) by some tangled
mathematical arguments,
but he was not aware that
these equations hinge on a
new concept of space and
time Rationalised 2023-24
Physics
110
field vanish (become zero) if velocity and magnetic field are parallel
or anti-parallel The force acts in a (sideways) direction perpendicular
to both the velocity and the magnetic field |
1 | 3336-3339 | He derived a set of
transformation equations
(known
after
him,
as
Lorentz
transformation
equations) by some tangled
mathematical arguments,
but he was not aware that
these equations hinge on a
new concept of space and
time Rationalised 2023-24
Physics
110
field vanish (become zero) if velocity and magnetic field are parallel
or anti-parallel The force acts in a (sideways) direction perpendicular
to both the velocity and the magnetic field Its
direction is given by the screw rule or right hand
rule for vector (or cross) product as illustrated
in Fig |
1 | 3337-3340 | Rationalised 2023-24
Physics
110
field vanish (become zero) if velocity and magnetic field are parallel
or anti-parallel The force acts in a (sideways) direction perpendicular
to both the velocity and the magnetic field Its
direction is given by the screw rule or right hand
rule for vector (or cross) product as illustrated
in Fig 4 |
1 | 3338-3341 | The force acts in a (sideways) direction perpendicular
to both the velocity and the magnetic field Its
direction is given by the screw rule or right hand
rule for vector (or cross) product as illustrated
in Fig 4 2 |
1 | 3339-3342 | Its
direction is given by the screw rule or right hand
rule for vector (or cross) product as illustrated
in Fig 4 2 (iii)
The magnetic force is zero if charge is not
moving (as then |v|= 0) |
1 | 3340-3343 | 4 2 (iii)
The magnetic force is zero if charge is not
moving (as then |v|= 0) Only a moving
charge feels the magnetic force |
1 | 3341-3344 | 2 (iii)
The magnetic force is zero if charge is not
moving (as then |v|= 0) Only a moving
charge feels the magnetic force The expression for the magnetic force helps
us to define the unit of the magnetic field, if one
takes q, F and v, all to be unity in the force
equation F = q [ v × B] =q v B sin q ˆn , where q is
the angle between v and B [see Fig |
1 | 3342-3345 | (iii)
The magnetic force is zero if charge is not
moving (as then |v|= 0) Only a moving
charge feels the magnetic force The expression for the magnetic force helps
us to define the unit of the magnetic field, if one
takes q, F and v, all to be unity in the force
equation F = q [ v × B] =q v B sin q ˆn , where q is
the angle between v and B [see Fig 4 |
1 | 3343-3346 | Only a moving
charge feels the magnetic force The expression for the magnetic force helps
us to define the unit of the magnetic field, if one
takes q, F and v, all to be unity in the force
equation F = q [ v × B] =q v B sin q ˆn , where q is
the angle between v and B [see Fig 4 2 (a)] |
1 | 3344-3347 | The expression for the magnetic force helps
us to define the unit of the magnetic field, if one
takes q, F and v, all to be unity in the force
equation F = q [ v × B] =q v B sin q ˆn , where q is
the angle between v and B [see Fig 4 2 (a)] The
magnitude of magnetic field B is 1 SI unit, when
the force acting on a unit charge (1 C), moving
perpendicular to B with a speed 1m/s, is one
newton |
1 | 3345-3348 | 4 2 (a)] The
magnitude of magnetic field B is 1 SI unit, when
the force acting on a unit charge (1 C), moving
perpendicular to B with a speed 1m/s, is one
newton Dimensionally, we have [B] = [F/qv] and the unit
of B are Newton second / (coulomb metre) |
1 | 3346-3349 | 2 (a)] The
magnitude of magnetic field B is 1 SI unit, when
the force acting on a unit charge (1 C), moving
perpendicular to B with a speed 1m/s, is one
newton Dimensionally, we have [B] = [F/qv] and the unit
of B are Newton second / (coulomb metre) This unit is called tesla (T)
named after Nikola Tesla (1856 – 1943) |
1 | 3347-3350 | The
magnitude of magnetic field B is 1 SI unit, when
the force acting on a unit charge (1 C), moving
perpendicular to B with a speed 1m/s, is one
newton Dimensionally, we have [B] = [F/qv] and the unit
of B are Newton second / (coulomb metre) This unit is called tesla (T)
named after Nikola Tesla (1856 – 1943) Tesla is a rather large unit |
1 | 3348-3351 | Dimensionally, we have [B] = [F/qv] and the unit
of B are Newton second / (coulomb metre) This unit is called tesla (T)
named after Nikola Tesla (1856 – 1943) Tesla is a rather large unit A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used |
1 | 3349-3352 | This unit is called tesla (T)
named after Nikola Tesla (1856 – 1943) Tesla is a rather large unit A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used The
earth’s magnetic field is about 3 |
1 | 3350-3353 | Tesla is a rather large unit A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used The
earth’s magnetic field is about 3 6 × 10–5 T |
1 | 3351-3354 | A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used The
earth’s magnetic field is about 3 6 × 10–5 T 4 |
1 | 3352-3355 | The
earth’s magnetic field is about 3 6 × 10–5 T 4 2 |
1 | 3353-3356 | 6 × 10–5 T 4 2 3 Magnetic force on a current-carrying conductor
We can extend the analysis for force due to magnetic field on a single
moving charge to a straight rod carrying current |
1 | 3354-3357 | 4 2 3 Magnetic force on a current-carrying conductor
We can extend the analysis for force due to magnetic field on a single
moving charge to a straight rod carrying current Consider a rod of a
uniform cross-sectional area A and length l |
1 | 3355-3358 | 2 3 Magnetic force on a current-carrying conductor
We can extend the analysis for force due to magnetic field on a single
moving charge to a straight rod carrying current Consider a rod of a
uniform cross-sectional area A and length l We shall assume one kind
of mobile carriers as in a conductor (here electrons) |
1 | 3356-3359 | 3 Magnetic force on a current-carrying conductor
We can extend the analysis for force due to magnetic field on a single
moving charge to a straight rod carrying current Consider a rod of a
uniform cross-sectional area A and length l We shall assume one kind
of mobile carriers as in a conductor (here electrons) Let the number
density of these mobile charge carriers in it be n |
1 | 3357-3360 | Consider a rod of a
uniform cross-sectional area A and length l We shall assume one kind
of mobile carriers as in a conductor (here electrons) Let the number
density of these mobile charge carriers in it be n Then the total number
of mobile charge carriers in it is nlA |
1 | 3358-3361 | We shall assume one kind
of mobile carriers as in a conductor (here electrons) Let the number
density of these mobile charge carriers in it be n Then the total number
of mobile charge carriers in it is nlA For a steady current I in this
conducting rod, we may assume that each mobile carrier has an average
drift velocity vd (see Chapter 3) |
1 | 3359-3362 | Let the number
density of these mobile charge carriers in it be n Then the total number
of mobile charge carriers in it is nlA For a steady current I in this
conducting rod, we may assume that each mobile carrier has an average
drift velocity vd (see Chapter 3) In the presence of an external magnetic
field B, the force on these carriers is:
F = (nlA)q vd ´´´´´ B
where q is the value of the charge on a carrier |
1 | 3360-3363 | Then the total number
of mobile charge carriers in it is nlA For a steady current I in this
conducting rod, we may assume that each mobile carrier has an average
drift velocity vd (see Chapter 3) In the presence of an external magnetic
field B, the force on these carriers is:
F = (nlA)q vd ´´´´´ B
where q is the value of the charge on a carrier Now nq vd is the current
density j and |(nq vd)|A is the current I (see Chapter 3 for the discussion
of current and current density) |
1 | 3361-3364 | For a steady current I in this
conducting rod, we may assume that each mobile carrier has an average
drift velocity vd (see Chapter 3) In the presence of an external magnetic
field B, the force on these carriers is:
F = (nlA)q vd ´´´´´ B
where q is the value of the charge on a carrier Now nq vd is the current
density j and |(nq vd)|A is the current I (see Chapter 3 for the discussion
of current and current density) Thus,
F = [(nq vd )lA] × B = [ jAl ] ´´´´´ B
= Il ´´´´´ B
(4 |
1 | 3362-3365 | In the presence of an external magnetic
field B, the force on these carriers is:
F = (nlA)q vd ´´´´´ B
where q is the value of the charge on a carrier Now nq vd is the current
density j and |(nq vd)|A is the current I (see Chapter 3 for the discussion
of current and current density) Thus,
F = [(nq vd )lA] × B = [ jAl ] ´´´´´ B
= Il ´´´´´ B
(4 4)
where l is a vector of magnitude l, the length of the rod, and with a direction
identical to the current I |
1 | 3363-3366 | Now nq vd is the current
density j and |(nq vd)|A is the current I (see Chapter 3 for the discussion
of current and current density) Thus,
F = [(nq vd )lA] × B = [ jAl ] ´´´´´ B
= Il ´´´´´ B
(4 4)
where l is a vector of magnitude l, the length of the rod, and with a direction
identical to the current I Note that the current I is not a vector |
1 | 3364-3367 | Thus,
F = [(nq vd )lA] × B = [ jAl ] ´´´´´ B
= Il ´´´´´ B
(4 4)
where l is a vector of magnitude l, the length of the rod, and with a direction
identical to the current I Note that the current I is not a vector In the last
step leading to Eq |
1 | 3365-3368 | 4)
where l is a vector of magnitude l, the length of the rod, and with a direction
identical to the current I Note that the current I is not a vector In the last
step leading to Eq (4 |
1 | 3366-3369 | Note that the current I is not a vector In the last
step leading to Eq (4 4), we have transferred the vector sign from j to l |
1 | 3367-3370 | In the last
step leading to Eq (4 4), we have transferred the vector sign from j to l Equation (4 |
1 | 3368-3371 | (4 4), we have transferred the vector sign from j to l Equation (4 4) holds for a straight rod |
1 | 3369-3372 | 4), we have transferred the vector sign from j to l Equation (4 4) holds for a straight rod In this equation, B is the
external magnetic field |
1 | 3370-3373 | Equation (4 4) holds for a straight rod In this equation, B is the
external magnetic field It is not the field produced by the current-carrying
rod |
1 | 3371-3374 | 4) holds for a straight rod In this equation, B is the
external magnetic field It is not the field produced by the current-carrying
rod If the wire has an arbitrary shape we can calculate the Lorentz force
on it by considering it as a collection of linear strips dlj and summing
j
j
Id
×
F
B
l
This summation can be converted to an integral in most cases |
1 | 3372-3375 | In this equation, B is the
external magnetic field It is not the field produced by the current-carrying
rod If the wire has an arbitrary shape we can calculate the Lorentz force
on it by considering it as a collection of linear strips dlj and summing
j
j
Id
×
F
B
l
This summation can be converted to an integral in most cases FIGURE 4 |
1 | 3373-3376 | It is not the field produced by the current-carrying
rod If the wire has an arbitrary shape we can calculate the Lorentz force
on it by considering it as a collection of linear strips dlj and summing
j
j
Id
×
F
B
l
This summation can be converted to an integral in most cases FIGURE 4 2 The direction of the magnetic
force acting on a charged particle |
1 | 3374-3377 | If the wire has an arbitrary shape we can calculate the Lorentz force
on it by considering it as a collection of linear strips dlj and summing
j
j
Id
×
F
B
l
This summation can be converted to an integral in most cases FIGURE 4 2 The direction of the magnetic
force acting on a charged particle (a) The
force on a positively charged particle with
velocity v and making an angle q with the
magnetic field B is given by the right-hand
rule |
1 | 3375-3378 | FIGURE 4 2 The direction of the magnetic
force acting on a charged particle (a) The
force on a positively charged particle with
velocity v and making an angle q with the
magnetic field B is given by the right-hand
rule (b) A moving charged particle q is
deflected in an opposite sense to –q in the
presence of magnetic field |
1 | 3376-3379 | 2 The direction of the magnetic
force acting on a charged particle (a) The
force on a positively charged particle with
velocity v and making an angle q with the
magnetic field B is given by the right-hand
rule (b) A moving charged particle q is
deflected in an opposite sense to –q in the
presence of magnetic field Rationalised 2023-24
111
Moving Charges and
Magnetism
EXAMPLE 4 |
1 | 3377-3380 | (a) The
force on a positively charged particle with
velocity v and making an angle q with the
magnetic field B is given by the right-hand
rule (b) A moving charged particle q is
deflected in an opposite sense to –q in the
presence of magnetic field Rationalised 2023-24
111
Moving Charges and
Magnetism
EXAMPLE 4 1
Example 4 |
1 | 3378-3381 | (b) A moving charged particle q is
deflected in an opposite sense to –q in the
presence of magnetic field Rationalised 2023-24
111
Moving Charges and
Magnetism
EXAMPLE 4 1
Example 4 1 A straight wire of mass 200 g and length 1 |
1 | 3379-3382 | Rationalised 2023-24
111
Moving Charges and
Magnetism
EXAMPLE 4 1
Example 4 1 A straight wire of mass 200 g and length 1 5 m carries
a current of 2 A |
1 | 3380-3383 | 1
Example 4 1 A straight wire of mass 200 g and length 1 5 m carries
a current of 2 A It is suspended in mid-air by a uniform horizontal
magnetic field B (Fig |
1 | 3381-3384 | 1 A straight wire of mass 200 g and length 1 5 m carries
a current of 2 A It is suspended in mid-air by a uniform horizontal
magnetic field B (Fig 4 |
1 | 3382-3385 | 5 m carries
a current of 2 A It is suspended in mid-air by a uniform horizontal
magnetic field B (Fig 4 3) |
1 | 3383-3386 | It is suspended in mid-air by a uniform horizontal
magnetic field B (Fig 4 3) What is the magnitude of the magnetic
field |
1 | 3384-3387 | 4 3) What is the magnitude of the magnetic
field FIGURE 4 |
1 | 3385-3388 | 3) What is the magnitude of the magnetic
field FIGURE 4 3
Solution From Eq |
1 | 3386-3389 | What is the magnitude of the magnetic
field FIGURE 4 3
Solution From Eq (4 |
1 | 3387-3390 | FIGURE 4 3
Solution From Eq (4 4), we find that there is an upward force F, of
magnitude IlB, |
1 | 3388-3391 | 3
Solution From Eq (4 4), we find that there is an upward force F, of
magnitude IlB, For mid-air suspension, this must be balanced by
the force due to gravity:
m g = I lB
m g
B
I l
=
0 |
1 | 3389-3392 | (4 4), we find that there is an upward force F, of
magnitude IlB, For mid-air suspension, this must be balanced by
the force due to gravity:
m g = I lB
m g
B
I l
=
0 2
9 |
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