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1 | 390-393 | It follows straight from the fact
that Coulomb’s law is consistent with Newton’s third law The proof
is left to you as an exercise 1 7 ELECTRIC FIELD
Let us consider a point charge Q placed in vacuum, at the origin O |
1 | 391-394 | The proof
is left to you as an exercise 1 7 ELECTRIC FIELD
Let us consider a point charge Q placed in vacuum, at the origin O If we
place another point charge q at a point P, where OP = r, then the charge Q
will exert a force on q as per Coulomb’s law |
1 | 392-395 | 1 7 ELECTRIC FIELD
Let us consider a point charge Q placed in vacuum, at the origin O If we
place another point charge q at a point P, where OP = r, then the charge Q
will exert a force on q as per Coulomb’s law We may ask the question: If
charge q is removed, then what is left in the surrounding |
1 | 393-396 | 7 ELECTRIC FIELD
Let us consider a point charge Q placed in vacuum, at the origin O If we
place another point charge q at a point P, where OP = r, then the charge Q
will exert a force on q as per Coulomb’s law We may ask the question: If
charge q is removed, then what is left in the surrounding Is there
nothing |
1 | 394-397 | If we
place another point charge q at a point P, where OP = r, then the charge Q
will exert a force on q as per Coulomb’s law We may ask the question: If
charge q is removed, then what is left in the surrounding Is there
nothing If there is nothing at the point P, then how does a force act
when we place the charge q at P |
1 | 395-398 | We may ask the question: If
charge q is removed, then what is left in the surrounding Is there
nothing If there is nothing at the point P, then how does a force act
when we place the charge q at P In order to answer such questions, the
early scientists introduced the concept of field |
1 | 396-399 | Is there
nothing If there is nothing at the point P, then how does a force act
when we place the charge q at P In order to answer such questions, the
early scientists introduced the concept of field According to this, we say
that the charge Q produces an electric field everywhere in the surrounding |
1 | 397-400 | If there is nothing at the point P, then how does a force act
when we place the charge q at P In order to answer such questions, the
early scientists introduced the concept of field According to this, we say
that the charge Q produces an electric field everywhere in the surrounding When another charge q is brought at some point P, the field there acts on
it and produces a force |
1 | 398-401 | In order to answer such questions, the
early scientists introduced the concept of field According to this, we say
that the charge Q produces an electric field everywhere in the surrounding When another charge q is brought at some point P, the field there acts on
it and produces a force The electric field produced by the charge Q at a
point r is given as
E r
r
r
( ) =
=
41
41
0
2
0
2
π
π
ε
ε
rQ
rQ
ˆ
ˆ
(1 |
1 | 399-402 | According to this, we say
that the charge Q produces an electric field everywhere in the surrounding When another charge q is brought at some point P, the field there acts on
it and produces a force The electric field produced by the charge Q at a
point r is given as
E r
r
r
( ) =
=
41
41
0
2
0
2
π
π
ε
ε
rQ
rQ
ˆ
ˆ
(1 6)
where ˆ =
r
r/r, is a unit vector from the origin to the point r |
1 | 400-403 | When another charge q is brought at some point P, the field there acts on
it and produces a force The electric field produced by the charge Q at a
point r is given as
E r
r
r
( ) =
=
41
41
0
2
0
2
π
π
ε
ε
rQ
rQ
ˆ
ˆ
(1 6)
where ˆ =
r
r/r, is a unit vector from the origin to the point r Thus, Eq |
1 | 401-404 | The electric field produced by the charge Q at a
point r is given as
E r
r
r
( ) =
=
41
41
0
2
0
2
π
π
ε
ε
rQ
rQ
ˆ
ˆ
(1 6)
where ˆ =
r
r/r, is a unit vector from the origin to the point r Thus, Eq (1 |
1 | 402-405 | 6)
where ˆ =
r
r/r, is a unit vector from the origin to the point r Thus, Eq (1 6)
specifies the value of the electric field for each value of the position
vector r |
1 | 403-406 | Thus, Eq (1 6)
specifies the value of the electric field for each value of the position
vector r The word “field” signifies how some distributed quantity (which
could be a scalar or a vector) varies with position |
1 | 404-407 | (1 6)
specifies the value of the electric field for each value of the position
vector r The word “field” signifies how some distributed quantity (which
could be a scalar or a vector) varies with position The effect of the charge
has been incorporated in the existence of the electric field |
1 | 405-408 | 6)
specifies the value of the electric field for each value of the position
vector r The word “field” signifies how some distributed quantity (which
could be a scalar or a vector) varies with position The effect of the charge
has been incorporated in the existence of the electric field We obtain the
force F exerted by a charge Q on a charge q, as
F
r
=
41
0
2
πε
rQq
ˆ
(1 |
1 | 406-409 | The word “field” signifies how some distributed quantity (which
could be a scalar or a vector) varies with position The effect of the charge
has been incorporated in the existence of the electric field We obtain the
force F exerted by a charge Q on a charge q, as
F
r
=
41
0
2
πε
rQq
ˆ
(1 7)
Note that the charge q also exerts an equal and opposite force on the
charge Q |
1 | 407-410 | The effect of the charge
has been incorporated in the existence of the electric field We obtain the
force F exerted by a charge Q on a charge q, as
F
r
=
41
0
2
πε
rQq
ˆ
(1 7)
Note that the charge q also exerts an equal and opposite force on the
charge Q The electrostatic force between the charges Q and q can be
looked upon as an interaction between charge q and the electric field of
Q and vice versa |
1 | 408-411 | We obtain the
force F exerted by a charge Q on a charge q, as
F
r
=
41
0
2
πε
rQq
ˆ
(1 7)
Note that the charge q also exerts an equal and opposite force on the
charge Q The electrostatic force between the charges Q and q can be
looked upon as an interaction between charge q and the electric field of
Q and vice versa If we denote the position of charge q by the vector r, it
experiences a force F equal to the charge q multiplied by the electric
field E at the location of q |
1 | 409-412 | 7)
Note that the charge q also exerts an equal and opposite force on the
charge Q The electrostatic force between the charges Q and q can be
looked upon as an interaction between charge q and the electric field of
Q and vice versa If we denote the position of charge q by the vector r, it
experiences a force F equal to the charge q multiplied by the electric
field E at the location of q Thus,
F(r) = q E(r)
(1 |
1 | 410-413 | The electrostatic force between the charges Q and q can be
looked upon as an interaction between charge q and the electric field of
Q and vice versa If we denote the position of charge q by the vector r, it
experiences a force F equal to the charge q multiplied by the electric
field E at the location of q Thus,
F(r) = q E(r)
(1 8)
Equation (1 |
1 | 411-414 | If we denote the position of charge q by the vector r, it
experiences a force F equal to the charge q multiplied by the electric
field E at the location of q Thus,
F(r) = q E(r)
(1 8)
Equation (1 8) defines the SI unit of electric field as N/C* |
1 | 412-415 | Thus,
F(r) = q E(r)
(1 8)
Equation (1 8) defines the SI unit of electric field as N/C* Some important remarks may be made here:
(i)
From Eq |
1 | 413-416 | 8)
Equation (1 8) defines the SI unit of electric field as N/C* Some important remarks may be made here:
(i)
From Eq (1 |
1 | 414-417 | 8) defines the SI unit of electric field as N/C* Some important remarks may be made here:
(i)
From Eq (1 8), we can infer that if q is unity, the electric field due to
a charge Q is numerically equal to the force exerted by it |
1 | 415-418 | Some important remarks may be made here:
(i)
From Eq (1 8), we can infer that if q is unity, the electric field due to
a charge Q is numerically equal to the force exerted by it Thus, the
electric field due to a charge Q at a point in space may be defined
as the force that a unit positive charge would experience if placed
*
An alternate unit V/m will be introduced in the next chapter |
1 | 416-419 | (1 8), we can infer that if q is unity, the electric field due to
a charge Q is numerically equal to the force exerted by it Thus, the
electric field due to a charge Q at a point in space may be defined
as the force that a unit positive charge would experience if placed
*
An alternate unit V/m will be introduced in the next chapter FIGURE 1 |
1 | 417-420 | 8), we can infer that if q is unity, the electric field due to
a charge Q is numerically equal to the force exerted by it Thus, the
electric field due to a charge Q at a point in space may be defined
as the force that a unit positive charge would experience if placed
*
An alternate unit V/m will be introduced in the next chapter FIGURE 1 8 Electric
field (a) due to a
charge Q, (b) due to a
charge –Q |
1 | 418-421 | Thus, the
electric field due to a charge Q at a point in space may be defined
as the force that a unit positive charge would experience if placed
*
An alternate unit V/m will be introduced in the next chapter FIGURE 1 8 Electric
field (a) due to a
charge Q, (b) due to a
charge –Q Rationalised 2023-24
Electric Charges
and Fields
15
at that point |
1 | 419-422 | FIGURE 1 8 Electric
field (a) due to a
charge Q, (b) due to a
charge –Q Rationalised 2023-24
Electric Charges
and Fields
15
at that point The charge Q, which is producing the electric field, is
called a source charge and the charge q, which tests the effect of a
source charge, is called a test charge |
1 | 420-423 | 8 Electric
field (a) due to a
charge Q, (b) due to a
charge –Q Rationalised 2023-24
Electric Charges
and Fields
15
at that point The charge Q, which is producing the electric field, is
called a source charge and the charge q, which tests the effect of a
source charge, is called a test charge Note that the source charge Q
must remain at its original location |
1 | 421-424 | Rationalised 2023-24
Electric Charges
and Fields
15
at that point The charge Q, which is producing the electric field, is
called a source charge and the charge q, which tests the effect of a
source charge, is called a test charge Note that the source charge Q
must remain at its original location However, if a charge q is brought
at any point around Q, Q itself is bound to experience an electrical
force due to q and will tend to move |
1 | 422-425 | The charge Q, which is producing the electric field, is
called a source charge and the charge q, which tests the effect of a
source charge, is called a test charge Note that the source charge Q
must remain at its original location However, if a charge q is brought
at any point around Q, Q itself is bound to experience an electrical
force due to q and will tend to move A way out of this difficulty is to
make q negligibly small |
1 | 423-426 | Note that the source charge Q
must remain at its original location However, if a charge q is brought
at any point around Q, Q itself is bound to experience an electrical
force due to q and will tend to move A way out of this difficulty is to
make q negligibly small The force F is then negligibly small but the
ratio F/q is finite and defines the electric field:
E
F
=
→
qlim
q
0
(1 |
1 | 424-427 | However, if a charge q is brought
at any point around Q, Q itself is bound to experience an electrical
force due to q and will tend to move A way out of this difficulty is to
make q negligibly small The force F is then negligibly small but the
ratio F/q is finite and defines the electric field:
E
F
=
→
qlim
q
0
(1 9)
A practical way to get around the problem (of keeping Q undisturbed
in the presence of q) is to hold Q to its location by unspecified forces |
1 | 425-428 | A way out of this difficulty is to
make q negligibly small The force F is then negligibly small but the
ratio F/q is finite and defines the electric field:
E
F
=
→
qlim
q
0
(1 9)
A practical way to get around the problem (of keeping Q undisturbed
in the presence of q) is to hold Q to its location by unspecified forces This may look strange but actually this is what happens in practice |
1 | 426-429 | The force F is then negligibly small but the
ratio F/q is finite and defines the electric field:
E
F
=
→
qlim
q
0
(1 9)
A practical way to get around the problem (of keeping Q undisturbed
in the presence of q) is to hold Q to its location by unspecified forces This may look strange but actually this is what happens in practice When we are considering the electric force on a test charge q due to a
charged planar sheet (Section 1 |
1 | 427-430 | 9)
A practical way to get around the problem (of keeping Q undisturbed
in the presence of q) is to hold Q to its location by unspecified forces This may look strange but actually this is what happens in practice When we are considering the electric force on a test charge q due to a
charged planar sheet (Section 1 14), the charges on the sheet are held to
their locations by the forces due to the unspecified charged constituents
inside the sheet |
1 | 428-431 | This may look strange but actually this is what happens in practice When we are considering the electric force on a test charge q due to a
charged planar sheet (Section 1 14), the charges on the sheet are held to
their locations by the forces due to the unspecified charged constituents
inside the sheet (ii) Note that the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q |
1 | 429-432 | When we are considering the electric force on a test charge q due to a
charged planar sheet (Section 1 14), the charges on the sheet are held to
their locations by the forces due to the unspecified charged constituents
inside the sheet (ii) Note that the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q This is because
F is proportional to q, so the ratio F/q does not depend on q |
1 | 430-433 | 14), the charges on the sheet are held to
their locations by the forces due to the unspecified charged constituents
inside the sheet (ii) Note that the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q This is because
F is proportional to q, so the ratio F/q does not depend on q The
force F on the charge q due to the charge Q depends on the particular
location of charge q which may take any value in the space around
the charge Q |
1 | 431-434 | (ii) Note that the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q This is because
F is proportional to q, so the ratio F/q does not depend on q The
force F on the charge q due to the charge Q depends on the particular
location of charge q which may take any value in the space around
the charge Q Thus, the electric field E due to Q is also dependent on
the space coordinate r |
1 | 432-435 | This is because
F is proportional to q, so the ratio F/q does not depend on q The
force F on the charge q due to the charge Q depends on the particular
location of charge q which may take any value in the space around
the charge Q Thus, the electric field E due to Q is also dependent on
the space coordinate r For different positions of the charge q all over
the space, we get different values of electric field E |
1 | 433-436 | The
force F on the charge q due to the charge Q depends on the particular
location of charge q which may take any value in the space around
the charge Q Thus, the electric field E due to Q is also dependent on
the space coordinate r For different positions of the charge q all over
the space, we get different values of electric field E The field exists at
every point in three-dimensional space |
1 | 434-437 | Thus, the electric field E due to Q is also dependent on
the space coordinate r For different positions of the charge q all over
the space, we get different values of electric field E The field exists at
every point in three-dimensional space (iii) For a positive charge, the electric field will be directed radially
outwards from the charge |
1 | 435-438 | For different positions of the charge q all over
the space, we get different values of electric field E The field exists at
every point in three-dimensional space (iii) For a positive charge, the electric field will be directed radially
outwards from the charge On the other hand, if the source charge is
negative, the electric field vector, at each point, points radially inwards |
1 | 436-439 | The field exists at
every point in three-dimensional space (iii) For a positive charge, the electric field will be directed radially
outwards from the charge On the other hand, if the source charge is
negative, the electric field vector, at each point, points radially inwards (iv) Since the magnitude of the force F on charge q due to charge Q
depends only on the distance r of the charge q from charge Q,
the magnitude of the electric field E will also depend only on the
distance r |
1 | 437-440 | (iii) For a positive charge, the electric field will be directed radially
outwards from the charge On the other hand, if the source charge is
negative, the electric field vector, at each point, points radially inwards (iv) Since the magnitude of the force F on charge q due to charge Q
depends only on the distance r of the charge q from charge Q,
the magnitude of the electric field E will also depend only on the
distance r Thus at equal distances from the charge Q, the magnitude
of its electric field E is same |
1 | 438-441 | On the other hand, if the source charge is
negative, the electric field vector, at each point, points radially inwards (iv) Since the magnitude of the force F on charge q due to charge Q
depends only on the distance r of the charge q from charge Q,
the magnitude of the electric field E will also depend only on the
distance r Thus at equal distances from the charge Q, the magnitude
of its electric field E is same The magnitude of electric field E due to
a point charge is thus same on a sphere with the point charge at its
centre; in other words, it has a spherical symmetry |
1 | 439-442 | (iv) Since the magnitude of the force F on charge q due to charge Q
depends only on the distance r of the charge q from charge Q,
the magnitude of the electric field E will also depend only on the
distance r Thus at equal distances from the charge Q, the magnitude
of its electric field E is same The magnitude of electric field E due to
a point charge is thus same on a sphere with the point charge at its
centre; in other words, it has a spherical symmetry 1 |
1 | 440-443 | Thus at equal distances from the charge Q, the magnitude
of its electric field E is same The magnitude of electric field E due to
a point charge is thus same on a sphere with the point charge at its
centre; in other words, it has a spherical symmetry 1 7 |
1 | 441-444 | The magnitude of electric field E due to
a point charge is thus same on a sphere with the point charge at its
centre; in other words, it has a spherical symmetry 1 7 1 Electric field due to a system of charges
Consider a system of charges q1, q2, |
1 | 442-445 | 1 7 1 Electric field due to a system of charges
Consider a system of charges q1, q2, , qn with position vectors r1,
r2, |
1 | 443-446 | 7 1 Electric field due to a system of charges
Consider a system of charges q1, q2, , qn with position vectors r1,
r2, , rn relative to some origin O |
1 | 444-447 | 1 Electric field due to a system of charges
Consider a system of charges q1, q2, , qn with position vectors r1,
r2, , rn relative to some origin O Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges q1, q2, |
1 | 445-448 | , qn with position vectors r1,
r2, , rn relative to some origin O Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges q1, q2, , qn |
1 | 446-449 | , rn relative to some origin O Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges q1, q2, , qn We can use Coulomb’s law and the
superposition principle to determine this field at a point P denoted by
position vector r |
1 | 447-450 | Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges q1, q2, , qn We can use Coulomb’s law and the
superposition principle to determine this field at a point P denoted by
position vector r Rationalised 2023-24
16
Physics
Electric field E1 at r due to q1 at r1 is given by
E1 =
41
0
1
1
2
πε
q
r P
1P
ˆr
where
1P
ˆr is a unit vector in the direction from q1 to P,
and r1P is the distance between q1 and P |
1 | 448-451 | , qn We can use Coulomb’s law and the
superposition principle to determine this field at a point P denoted by
position vector r Rationalised 2023-24
16
Physics
Electric field E1 at r due to q1 at r1 is given by
E1 =
41
0
1
1
2
πε
q
r P
1P
ˆr
where
1P
ˆr is a unit vector in the direction from q1 to P,
and r1P is the distance between q1 and P In the same manner, electric field E2 at r due to q2 at
r2 is
E2 =
41
0
2
2
2
πε
q
r P
2P
ˆr
where
ˆr2P
is a unit vector in the direction from q2 to P
and r2P is the distance between q2 and P |
1 | 449-452 | We can use Coulomb’s law and the
superposition principle to determine this field at a point P denoted by
position vector r Rationalised 2023-24
16
Physics
Electric field E1 at r due to q1 at r1 is given by
E1 =
41
0
1
1
2
πε
q
r P
1P
ˆr
where
1P
ˆr is a unit vector in the direction from q1 to P,
and r1P is the distance between q1 and P In the same manner, electric field E2 at r due to q2 at
r2 is
E2 =
41
0
2
2
2
πε
q
r P
2P
ˆr
where
ˆr2P
is a unit vector in the direction from q2 to P
and r2P is the distance between q2 and P Similar
expressions hold good for fields E3, E4, |
1 | 450-453 | Rationalised 2023-24
16
Physics
Electric field E1 at r due to q1 at r1 is given by
E1 =
41
0
1
1
2
πε
q
r P
1P
ˆr
where
1P
ˆr is a unit vector in the direction from q1 to P,
and r1P is the distance between q1 and P In the same manner, electric field E2 at r due to q2 at
r2 is
E2 =
41
0
2
2
2
πε
q
r P
2P
ˆr
where
ˆr2P
is a unit vector in the direction from q2 to P
and r2P is the distance between q2 and P Similar
expressions hold good for fields E3, E4, , En due to
charges q3, q4, |
1 | 451-454 | In the same manner, electric field E2 at r due to q2 at
r2 is
E2 =
41
0
2
2
2
πε
q
r P
2P
ˆr
where
ˆr2P
is a unit vector in the direction from q2 to P
and r2P is the distance between q2 and P Similar
expressions hold good for fields E3, E4, , En due to
charges q3, q4, , qn |
1 | 452-455 | Similar
expressions hold good for fields E3, E4, , En due to
charges q3, q4, , qn By the superposition principle, the electric field E at r
due to the system of charges is (as shown in Fig |
1 | 453-456 | , En due to
charges q3, q4, , qn By the superposition principle, the electric field E at r
due to the system of charges is (as shown in Fig 1 |
1 | 454-457 | , qn By the superposition principle, the electric field E at r
due to the system of charges is (as shown in Fig 1 9)
E(r) = E1 (r) + E2 (r) + … + En(r)
=
41
41
41
0
1
1
2
1
0
2
2
2
2
0
2
π
π
π
ε
ε
ε
rq
rq
q
r
n
n
n
P
P
P
P
P
P
ˆ
ˆ |
1 | 455-458 | By the superposition principle, the electric field E at r
due to the system of charges is (as shown in Fig 1 9)
E(r) = E1 (r) + E2 (r) + … + En(r)
=
41
41
41
0
1
1
2
1
0
2
2
2
2
0
2
π
π
π
ε
ε
ε
rq
rq
q
r
n
n
n
P
P
P
P
P
P
ˆ
ˆ ˆ
r
r
r
+
+
+
E(r) =
=∑
41
0
P
i P
πε
q
r
i
i
i
n
2
1
ˆr
(1 |
1 | 456-459 | 1 9)
E(r) = E1 (r) + E2 (r) + … + En(r)
=
41
41
41
0
1
1
2
1
0
2
2
2
2
0
2
π
π
π
ε
ε
ε
rq
rq
q
r
n
n
n
P
P
P
P
P
P
ˆ
ˆ ˆ
r
r
r
+
+
+
E(r) =
=∑
41
0
P
i P
πε
q
r
i
i
i
n
2
1
ˆr
(1 10)
E is a vector quantity that varies from one point to another point in space
and is determined from the positions of the source charges |
1 | 457-460 | 9)
E(r) = E1 (r) + E2 (r) + … + En(r)
=
41
41
41
0
1
1
2
1
0
2
2
2
2
0
2
π
π
π
ε
ε
ε
rq
rq
q
r
n
n
n
P
P
P
P
P
P
ˆ
ˆ ˆ
r
r
r
+
+
+
E(r) =
=∑
41
0
P
i P
πε
q
r
i
i
i
n
2
1
ˆr
(1 10)
E is a vector quantity that varies from one point to another point in space
and is determined from the positions of the source charges 1 |
1 | 458-461 | ˆ
r
r
r
+
+
+
E(r) =
=∑
41
0
P
i P
πε
q
r
i
i
i
n
2
1
ˆr
(1 10)
E is a vector quantity that varies from one point to another point in space
and is determined from the positions of the source charges 1 7 |
1 | 459-462 | 10)
E is a vector quantity that varies from one point to another point in space
and is determined from the positions of the source charges 1 7 2 Physical significance of electric field
You may wonder why the notion of electric field has been introduced
here at all |
1 | 460-463 | 1 7 2 Physical significance of electric field
You may wonder why the notion of electric field has been introduced
here at all After all, for any system of charges, the measurable quantity
is the force on a charge which can be directly determined using Coulomb’s
law and the superposition principle [Eq |
1 | 461-464 | 7 2 Physical significance of electric field
You may wonder why the notion of electric field has been introduced
here at all After all, for any system of charges, the measurable quantity
is the force on a charge which can be directly determined using Coulomb’s
law and the superposition principle [Eq (1 |
1 | 462-465 | 2 Physical significance of electric field
You may wonder why the notion of electric field has been introduced
here at all After all, for any system of charges, the measurable quantity
is the force on a charge which can be directly determined using Coulomb’s
law and the superposition principle [Eq (1 5)] |
1 | 463-466 | After all, for any system of charges, the measurable quantity
is the force on a charge which can be directly determined using Coulomb’s
law and the superposition principle [Eq (1 5)] Why then introduce this
intermediate quantity called the electric field |
1 | 464-467 | (1 5)] Why then introduce this
intermediate quantity called the electric field For electrostatics, the concept of electric field is convenient, but not
really necessary |
1 | 465-468 | 5)] Why then introduce this
intermediate quantity called the electric field For electrostatics, the concept of electric field is convenient, but not
really necessary Electric field is an elegant way of characterising the
electrical environment of a system of charges |
1 | 466-469 | Why then introduce this
intermediate quantity called the electric field For electrostatics, the concept of electric field is convenient, but not
really necessary Electric field is an elegant way of characterising the
electrical environment of a system of charges Electric field at a point in
the space around a system of charges tells you the force a unit positive
test charge would experience if placed at that point (without disturbing
the system) |
1 | 467-470 | For electrostatics, the concept of electric field is convenient, but not
really necessary Electric field is an elegant way of characterising the
electrical environment of a system of charges Electric field at a point in
the space around a system of charges tells you the force a unit positive
test charge would experience if placed at that point (without disturbing
the system) Electric field is a characteristic of the system of charges and
is independent of the test charge that you place at a point to determine
the field |
1 | 468-471 | Electric field is an elegant way of characterising the
electrical environment of a system of charges Electric field at a point in
the space around a system of charges tells you the force a unit positive
test charge would experience if placed at that point (without disturbing
the system) Electric field is a characteristic of the system of charges and
is independent of the test charge that you place at a point to determine
the field The term field in physics generally refers to a quantity that is
defined at every point in space and may vary from point to point |
1 | 469-472 | Electric field at a point in
the space around a system of charges tells you the force a unit positive
test charge would experience if placed at that point (without disturbing
the system) Electric field is a characteristic of the system of charges and
is independent of the test charge that you place at a point to determine
the field The term field in physics generally refers to a quantity that is
defined at every point in space and may vary from point to point Electric
field is a vector field, since force is a vector quantity |
1 | 470-473 | Electric field is a characteristic of the system of charges and
is independent of the test charge that you place at a point to determine
the field The term field in physics generally refers to a quantity that is
defined at every point in space and may vary from point to point Electric
field is a vector field, since force is a vector quantity The true physical significance of the concept of electric field, however,
emerges only when we go beyond electrostatics and deal with time-
dependent electromagnetic phenomena |
1 | 471-474 | The term field in physics generally refers to a quantity that is
defined at every point in space and may vary from point to point Electric
field is a vector field, since force is a vector quantity The true physical significance of the concept of electric field, however,
emerges only when we go beyond electrostatics and deal with time-
dependent electromagnetic phenomena Suppose we consider the force
between two distant charges q1, q2 in accelerated motion |
1 | 472-475 | Electric
field is a vector field, since force is a vector quantity The true physical significance of the concept of electric field, however,
emerges only when we go beyond electrostatics and deal with time-
dependent electromagnetic phenomena Suppose we consider the force
between two distant charges q1, q2 in accelerated motion Now the greatest
speed with which a signal or information can go from one point to another
is c, the speed of light |
1 | 473-476 | The true physical significance of the concept of electric field, however,
emerges only when we go beyond electrostatics and deal with time-
dependent electromagnetic phenomena Suppose we consider the force
between two distant charges q1, q2 in accelerated motion Now the greatest
speed with which a signal or information can go from one point to another
is c, the speed of light Thus, the effect of any motion of q1 on q2 cannot
FIGURE 1 |
1 | 474-477 | Suppose we consider the force
between two distant charges q1, q2 in accelerated motion Now the greatest
speed with which a signal or information can go from one point to another
is c, the speed of light Thus, the effect of any motion of q1 on q2 cannot
FIGURE 1 9 Electric field at a point
due to a system of charges is the
vector sum of the electric fields at
the point due to individual charges |
1 | 475-478 | Now the greatest
speed with which a signal or information can go from one point to another
is c, the speed of light Thus, the effect of any motion of q1 on q2 cannot
FIGURE 1 9 Electric field at a point
due to a system of charges is the
vector sum of the electric fields at
the point due to individual charges Rationalised 2023-24
Electric Charges
and Fields
17
arise instantaneously |
1 | 476-479 | Thus, the effect of any motion of q1 on q2 cannot
FIGURE 1 9 Electric field at a point
due to a system of charges is the
vector sum of the electric fields at
the point due to individual charges Rationalised 2023-24
Electric Charges
and Fields
17
arise instantaneously There will be some time delay between the effect
(force on q2) and the cause (motion of q1) |
1 | 477-480 | 9 Electric field at a point
due to a system of charges is the
vector sum of the electric fields at
the point due to individual charges Rationalised 2023-24
Electric Charges
and Fields
17
arise instantaneously There will be some time delay between the effect
(force on q2) and the cause (motion of q1) It is precisely here that the
notion of electric field (strictly, electromagnetic field) is natural and very
useful |
1 | 478-481 | Rationalised 2023-24
Electric Charges
and Fields
17
arise instantaneously There will be some time delay between the effect
(force on q2) and the cause (motion of q1) It is precisely here that the
notion of electric field (strictly, electromagnetic field) is natural and very
useful The field picture is this: the accelerated motion of charge q1
produces electromagnetic waves, which then propagate with the speed
c, reach q2 and cause a force on q2 |
1 | 479-482 | There will be some time delay between the effect
(force on q2) and the cause (motion of q1) It is precisely here that the
notion of electric field (strictly, electromagnetic field) is natural and very
useful The field picture is this: the accelerated motion of charge q1
produces electromagnetic waves, which then propagate with the speed
c, reach q2 and cause a force on q2 The notion of field elegantly accounts
for the time delay |
1 | 480-483 | It is precisely here that the
notion of electric field (strictly, electromagnetic field) is natural and very
useful The field picture is this: the accelerated motion of charge q1
produces electromagnetic waves, which then propagate with the speed
c, reach q2 and cause a force on q2 The notion of field elegantly accounts
for the time delay Thus, even though electric and magnetic fields can be
detected only by their effects (forces) on charges, they are regarded as
physical entities, not merely mathematical constructs |
1 | 481-484 | The field picture is this: the accelerated motion of charge q1
produces electromagnetic waves, which then propagate with the speed
c, reach q2 and cause a force on q2 The notion of field elegantly accounts
for the time delay Thus, even though electric and magnetic fields can be
detected only by their effects (forces) on charges, they are regarded as
physical entities, not merely mathematical constructs They have an
independent dynamics of their own, i |
1 | 482-485 | The notion of field elegantly accounts
for the time delay Thus, even though electric and magnetic fields can be
detected only by their effects (forces) on charges, they are regarded as
physical entities, not merely mathematical constructs They have an
independent dynamics of their own, i e |
1 | 483-486 | Thus, even though electric and magnetic fields can be
detected only by their effects (forces) on charges, they are regarded as
physical entities, not merely mathematical constructs They have an
independent dynamics of their own, i e , they evolve according to laws
of their own |
1 | 484-487 | They have an
independent dynamics of their own, i e , they evolve according to laws
of their own They can also transport energy |
1 | 485-488 | e , they evolve according to laws
of their own They can also transport energy Thus, a source of time-
dependent electromagnetic fields, turned on for a short interval of time
and then switched off, leaves behind propagating electromagnetic fields
transporting energy |
1 | 486-489 | , they evolve according to laws
of their own They can also transport energy Thus, a source of time-
dependent electromagnetic fields, turned on for a short interval of time
and then switched off, leaves behind propagating electromagnetic fields
transporting energy The concept of field was first introduced by Faraday
and is now among the central concepts in physics |
1 | 487-490 | They can also transport energy Thus, a source of time-
dependent electromagnetic fields, turned on for a short interval of time
and then switched off, leaves behind propagating electromagnetic fields
transporting energy The concept of field was first introduced by Faraday
and is now among the central concepts in physics Example 1 |
1 | 488-491 | Thus, a source of time-
dependent electromagnetic fields, turned on for a short interval of time
and then switched off, leaves behind propagating electromagnetic fields
transporting energy The concept of field was first introduced by Faraday
and is now among the central concepts in physics Example 1 7 An electron falls through a distance of 1 |
1 | 489-492 | The concept of field was first introduced by Faraday
and is now among the central concepts in physics Example 1 7 An electron falls through a distance of 1 5 cm in a
uniform electric field of magnitude 2 |
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