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1 | 190-193 | (1 1) Coulomb thought of the following simple way: Suppose the
charge on a metallic sphere is q If the sphere is put in contact
with an identical uncharged sphere, the charge will spread over
the two spheres |
1 | 191-194 | 1) Coulomb thought of the following simple way: Suppose the
charge on a metallic sphere is q If the sphere is put in contact
with an identical uncharged sphere, the charge will spread over
the two spheres By symmetry, the charge on each sphere will
be q/2* |
1 | 192-195 | Coulomb thought of the following simple way: Suppose the
charge on a metallic sphere is q If the sphere is put in contact
with an identical uncharged sphere, the charge will spread over
the two spheres By symmetry, the charge on each sphere will
be q/2* Repeating this process, we can get charges q/2, q/4,
etc |
1 | 193-196 | If the sphere is put in contact
with an identical uncharged sphere, the charge will spread over
the two spheres By symmetry, the charge on each sphere will
be q/2* Repeating this process, we can get charges q/2, q/4,
etc Coulomb varied the distance for a fixed pair of charges and
measured the force for different separations |
1 | 194-197 | By symmetry, the charge on each sphere will
be q/2* Repeating this process, we can get charges q/2, q/4,
etc Coulomb varied the distance for a fixed pair of charges and
measured the force for different separations He then varied the
charges in pairs, keeping the distance fixed for each pair |
1 | 195-198 | Repeating this process, we can get charges q/2, q/4,
etc Coulomb varied the distance for a fixed pair of charges and
measured the force for different separations He then varied the
charges in pairs, keeping the distance fixed for each pair Comparing forces for different pairs of charges at different
distances, Coulomb arrived at the relation, Eq |
1 | 196-199 | Coulomb varied the distance for a fixed pair of charges and
measured the force for different separations He then varied the
charges in pairs, keeping the distance fixed for each pair Comparing forces for different pairs of charges at different
distances, Coulomb arrived at the relation, Eq (1 |
1 | 197-200 | He then varied the
charges in pairs, keeping the distance fixed for each pair Comparing forces for different pairs of charges at different
distances, Coulomb arrived at the relation, Eq (1 1) |
1 | 198-201 | Comparing forces for different pairs of charges at different
distances, Coulomb arrived at the relation, Eq (1 1) Coulomb’s law, a simple mathematical statement, was
initially experimentally arrived at in the manner described
above |
1 | 199-202 | (1 1) Coulomb’s law, a simple mathematical statement, was
initially experimentally arrived at in the manner described
above While the original experiments established it at a
macroscopic scale, it has also been established down to
subatomic level (r ~ 10–10 m) |
1 | 200-203 | 1) Coulomb’s law, a simple mathematical statement, was
initially experimentally arrived at in the manner described
above While the original experiments established it at a
macroscopic scale, it has also been established down to
subatomic level (r ~ 10–10 m) Coulomb discovered his law without knowing the explicit
magnitude of the charge |
1 | 201-204 | Coulomb’s law, a simple mathematical statement, was
initially experimentally arrived at in the manner described
above While the original experiments established it at a
macroscopic scale, it has also been established down to
subatomic level (r ~ 10–10 m) Coulomb discovered his law without knowing the explicit
magnitude of the charge In fact, it is the other way round:
Coulomb’s law can now be employed to furnish a definition
for a unit of charge |
1 | 202-205 | While the original experiments established it at a
macroscopic scale, it has also been established down to
subatomic level (r ~ 10–10 m) Coulomb discovered his law without knowing the explicit
magnitude of the charge In fact, it is the other way round:
Coulomb’s law can now be employed to furnish a definition
for a unit of charge In the relation, Eq |
1 | 203-206 | Coulomb discovered his law without knowing the explicit
magnitude of the charge In fact, it is the other way round:
Coulomb’s law can now be employed to furnish a definition
for a unit of charge In the relation, Eq (1 |
1 | 204-207 | In fact, it is the other way round:
Coulomb’s law can now be employed to furnish a definition
for a unit of charge In the relation, Eq (1 1), k is so far
arbitrary |
1 | 205-208 | In the relation, Eq (1 1), k is so far
arbitrary We can choose any positive value of k |
1 | 206-209 | (1 1), k is so far
arbitrary We can choose any positive value of k The choice
of k determines the size of the unit of charge |
1 | 207-210 | 1), k is so far
arbitrary We can choose any positive value of k The choice
of k determines the size of the unit of charge In SI units, the
value of k is about 9 × 109
2
2
Nm
C |
1 | 208-211 | We can choose any positive value of k The choice
of k determines the size of the unit of charge In SI units, the
value of k is about 9 × 109
2
2
Nm
C The unit of charge that
results from this choice is called a coulomb which we defined
earlier in Section 1 |
1 | 209-212 | The choice
of k determines the size of the unit of charge In SI units, the
value of k is about 9 × 109
2
2
Nm
C The unit of charge that
results from this choice is called a coulomb which we defined
earlier in Section 1 4 |
1 | 210-213 | In SI units, the
value of k is about 9 × 109
2
2
Nm
C The unit of charge that
results from this choice is called a coulomb which we defined
earlier in Section 1 4 Putting this value of k in Eq |
1 | 211-214 | The unit of charge that
results from this choice is called a coulomb which we defined
earlier in Section 1 4 Putting this value of k in Eq (1 |
1 | 212-215 | 4 Putting this value of k in Eq (1 1), we
see that for q1 = q2 = 1 C, r = 1 m
F = 9 × 109 N
That is, 1 C is the charge that when placed at a distance
of 1 m from another charge of the same magnitude in vacuum
experiences an electrical force of repulsion of magnitude
*
A torsion balance is a sensitive device to measure force |
1 | 213-216 | Putting this value of k in Eq (1 1), we
see that for q1 = q2 = 1 C, r = 1 m
F = 9 × 109 N
That is, 1 C is the charge that when placed at a distance
of 1 m from another charge of the same magnitude in vacuum
experiences an electrical force of repulsion of magnitude
*
A torsion balance is a sensitive device to measure force It was also used later
by Cavendish to measure the very feeble gravitational force between two objects,
to verify Newton’s Law of Gravitation |
1 | 214-217 | (1 1), we
see that for q1 = q2 = 1 C, r = 1 m
F = 9 × 109 N
That is, 1 C is the charge that when placed at a distance
of 1 m from another charge of the same magnitude in vacuum
experiences an electrical force of repulsion of magnitude
*
A torsion balance is a sensitive device to measure force It was also used later
by Cavendish to measure the very feeble gravitational force between two objects,
to verify Newton’s Law of Gravitation *
Implicit in this is the assumption of additivity of charges and conservation:
two charges (q/2 each) add up to make a total charge q |
1 | 215-218 | 1), we
see that for q1 = q2 = 1 C, r = 1 m
F = 9 × 109 N
That is, 1 C is the charge that when placed at a distance
of 1 m from another charge of the same magnitude in vacuum
experiences an electrical force of repulsion of magnitude
*
A torsion balance is a sensitive device to measure force It was also used later
by Cavendish to measure the very feeble gravitational force between two objects,
to verify Newton’s Law of Gravitation *
Implicit in this is the assumption of additivity of charges and conservation:
two charges (q/2 each) add up to make a total charge q Charles Augustin de
Coulomb (1736 – 1806)
Coulomb, a French
physicist, began his
career as a military
engineer in the West
Indies |
1 | 216-219 | It was also used later
by Cavendish to measure the very feeble gravitational force between two objects,
to verify Newton’s Law of Gravitation *
Implicit in this is the assumption of additivity of charges and conservation:
two charges (q/2 each) add up to make a total charge q Charles Augustin de
Coulomb (1736 – 1806)
Coulomb, a French
physicist, began his
career as a military
engineer in the West
Indies In 1776, he
returned to Paris and
retired to a small estate
to do his scientific
research |
1 | 217-220 | *
Implicit in this is the assumption of additivity of charges and conservation:
two charges (q/2 each) add up to make a total charge q Charles Augustin de
Coulomb (1736 – 1806)
Coulomb, a French
physicist, began his
career as a military
engineer in the West
Indies In 1776, he
returned to Paris and
retired to a small estate
to do his scientific
research He invented a
torsion
balance
to
measure the quantity of
a force and used it for
determination of forces
of electric attraction or
repulsion between small
charged spheres |
1 | 218-221 | Charles Augustin de
Coulomb (1736 – 1806)
Coulomb, a French
physicist, began his
career as a military
engineer in the West
Indies In 1776, he
returned to Paris and
retired to a small estate
to do his scientific
research He invented a
torsion
balance
to
measure the quantity of
a force and used it for
determination of forces
of electric attraction or
repulsion between small
charged spheres He
thus arrived in 1785 at
the inverse square law
relation, now known as
Coulomb’s law |
1 | 219-222 | In 1776, he
returned to Paris and
retired to a small estate
to do his scientific
research He invented a
torsion
balance
to
measure the quantity of
a force and used it for
determination of forces
of electric attraction or
repulsion between small
charged spheres He
thus arrived in 1785 at
the inverse square law
relation, now known as
Coulomb’s law The law
had been anticipated by
Priestley and also by
Cavendish
earlier,
though
Cavendish
never published his
results |
1 | 220-223 | He invented a
torsion
balance
to
measure the quantity of
a force and used it for
determination of forces
of electric attraction or
repulsion between small
charged spheres He
thus arrived in 1785 at
the inverse square law
relation, now known as
Coulomb’s law The law
had been anticipated by
Priestley and also by
Cavendish
earlier,
though
Cavendish
never published his
results Coulomb also
found
the
inverse
square law of force
between unlike and like
magnetic poles |
1 | 221-224 | He
thus arrived in 1785 at
the inverse square law
relation, now known as
Coulomb’s law The law
had been anticipated by
Priestley and also by
Cavendish
earlier,
though
Cavendish
never published his
results Coulomb also
found
the
inverse
square law of force
between unlike and like
magnetic poles CHARLES AUGUSTIN DE COULOMB (1736 –1806)
Rationalised 2023-24
8
Physics
9 × 109 N |
1 | 222-225 | The law
had been anticipated by
Priestley and also by
Cavendish
earlier,
though
Cavendish
never published his
results Coulomb also
found
the
inverse
square law of force
between unlike and like
magnetic poles CHARLES AUGUSTIN DE COULOMB (1736 –1806)
Rationalised 2023-24
8
Physics
9 × 109 N One coulomb is evidently too big a unit to
be used |
1 | 223-226 | Coulomb also
found
the
inverse
square law of force
between unlike and like
magnetic poles CHARLES AUGUSTIN DE COULOMB (1736 –1806)
Rationalised 2023-24
8
Physics
9 × 109 N One coulomb is evidently too big a unit to
be used In practice, in electrostatics, one uses
smaller units like 1 mC or 1 mC |
1 | 224-227 | CHARLES AUGUSTIN DE COULOMB (1736 –1806)
Rationalised 2023-24
8
Physics
9 × 109 N One coulomb is evidently too big a unit to
be used In practice, in electrostatics, one uses
smaller units like 1 mC or 1 mC The constant k in Eq |
1 | 225-228 | One coulomb is evidently too big a unit to
be used In practice, in electrostatics, one uses
smaller units like 1 mC or 1 mC The constant k in Eq (1 |
1 | 226-229 | In practice, in electrostatics, one uses
smaller units like 1 mC or 1 mC The constant k in Eq (1 1) is usually put as
k = 1/4pe0 for later convenience, so that Coulomb’s
law is written as
0
1
2
2
1
4
q q
F
r
ε
=
π
(1 |
1 | 227-230 | The constant k in Eq (1 1) is usually put as
k = 1/4pe0 for later convenience, so that Coulomb’s
law is written as
0
1
2
2
1
4
q q
F
r
ε
=
π
(1 2)
e0 is called the permittivity of free space |
1 | 228-231 | (1 1) is usually put as
k = 1/4pe0 for later convenience, so that Coulomb’s
law is written as
0
1
2
2
1
4
q q
F
r
ε
=
π
(1 2)
e0 is called the permittivity of free space The value
of e0 in SI units is
0
= 8 |
1 | 229-232 | 1) is usually put as
k = 1/4pe0 for later convenience, so that Coulomb’s
law is written as
0
1
2
2
1
4
q q
F
r
ε
=
π
(1 2)
e0 is called the permittivity of free space The value
of e0 in SI units is
0
= 8 854 × 10–12 C2 N–1m–2
Since force is a vector, it is better to write
Coulomb’s law in the vector notation |
1 | 230-233 | 2)
e0 is called the permittivity of free space The value
of e0 in SI units is
0
= 8 854 × 10–12 C2 N–1m–2
Since force is a vector, it is better to write
Coulomb’s law in the vector notation Let the position
vectors of charges q1 and q2 be r1 and r2 respectively
[see Fig |
1 | 231-234 | The value
of e0 in SI units is
0
= 8 854 × 10–12 C2 N–1m–2
Since force is a vector, it is better to write
Coulomb’s law in the vector notation Let the position
vectors of charges q1 and q2 be r1 and r2 respectively
[see Fig 1 |
1 | 232-235 | 854 × 10–12 C2 N–1m–2
Since force is a vector, it is better to write
Coulomb’s law in the vector notation Let the position
vectors of charges q1 and q2 be r1 and r2 respectively
[see Fig 1 3(a)] |
1 | 233-236 | Let the position
vectors of charges q1 and q2 be r1 and r2 respectively
[see Fig 1 3(a)] We denote force on q1 due to q2 by
F12 and force on q2 due to q1 by F21 |
1 | 234-237 | 1 3(a)] We denote force on q1 due to q2 by
F12 and force on q2 due to q1 by F21 The two point
charges q1 and q2 have been numbered 1 and 2 for
convenience and the vector leading from 1 to 2 is
denoted by r21:
r21 = r2 – r1
In the same way, the vector leading from 2 to 1 is denoted by r12:
r12 = r1 – r2 = – r21
The magnitude of the vectors r21 and r12 is denoted by r21 and r12,
respectively (r12 = r21) |
1 | 235-238 | 3(a)] We denote force on q1 due to q2 by
F12 and force on q2 due to q1 by F21 The two point
charges q1 and q2 have been numbered 1 and 2 for
convenience and the vector leading from 1 to 2 is
denoted by r21:
r21 = r2 – r1
In the same way, the vector leading from 2 to 1 is denoted by r12:
r12 = r1 – r2 = – r21
The magnitude of the vectors r21 and r12 is denoted by r21 and r12,
respectively (r12 = r21) The direction of a vector is specified by a unit
vector along the vector |
1 | 236-239 | We denote force on q1 due to q2 by
F12 and force on q2 due to q1 by F21 The two point
charges q1 and q2 have been numbered 1 and 2 for
convenience and the vector leading from 1 to 2 is
denoted by r21:
r21 = r2 – r1
In the same way, the vector leading from 2 to 1 is denoted by r12:
r12 = r1 – r2 = – r21
The magnitude of the vectors r21 and r12 is denoted by r21 and r12,
respectively (r12 = r21) The direction of a vector is specified by a unit
vector along the vector To denote the direction from 1 to 2 (or from 2 to
1), we define the unit vectors:
ɵ
21
21
21
= r
r
r
, ɵ
ɵ
ɵ
12
12
21
12
12
,
=
−
r
r
r
r
r
Coulomb’s force law between two point charges q1 and q2 located at
r1 and r2, respectively is then expressed as
ɵ
1
2
21
21
2
21
41
ε
=
π
F
r
o
q
rq
(1 |
1 | 237-240 | The two point
charges q1 and q2 have been numbered 1 and 2 for
convenience and the vector leading from 1 to 2 is
denoted by r21:
r21 = r2 – r1
In the same way, the vector leading from 2 to 1 is denoted by r12:
r12 = r1 – r2 = – r21
The magnitude of the vectors r21 and r12 is denoted by r21 and r12,
respectively (r12 = r21) The direction of a vector is specified by a unit
vector along the vector To denote the direction from 1 to 2 (or from 2 to
1), we define the unit vectors:
ɵ
21
21
21
= r
r
r
, ɵ
ɵ
ɵ
12
12
21
12
12
,
=
−
r
r
r
r
r
Coulomb’s force law between two point charges q1 and q2 located at
r1 and r2, respectively is then expressed as
ɵ
1
2
21
21
2
21
41
ε
=
π
F
r
o
q
rq
(1 3)
Some remarks on Eq |
1 | 238-241 | The direction of a vector is specified by a unit
vector along the vector To denote the direction from 1 to 2 (or from 2 to
1), we define the unit vectors:
ɵ
21
21
21
= r
r
r
, ɵ
ɵ
ɵ
12
12
21
12
12
,
=
−
r
r
r
r
r
Coulomb’s force law between two point charges q1 and q2 located at
r1 and r2, respectively is then expressed as
ɵ
1
2
21
21
2
21
41
ε
=
π
F
r
o
q
rq
(1 3)
Some remarks on Eq (1 |
1 | 239-242 | To denote the direction from 1 to 2 (or from 2 to
1), we define the unit vectors:
ɵ
21
21
21
= r
r
r
, ɵ
ɵ
ɵ
12
12
21
12
12
,
=
−
r
r
r
r
r
Coulomb’s force law between two point charges q1 and q2 located at
r1 and r2, respectively is then expressed as
ɵ
1
2
21
21
2
21
41
ε
=
π
F
r
o
q
rq
(1 3)
Some remarks on Eq (1 3) are relevant:
·
Equation (1 |
1 | 240-243 | 3)
Some remarks on Eq (1 3) are relevant:
·
Equation (1 3) is valid for any sign of q1 and q2 whether positive or
negative |
1 | 241-244 | (1 3) are relevant:
·
Equation (1 3) is valid for any sign of q1 and q2 whether positive or
negative If q1 and q2 are of the same sign (either both positive or both
negative), F21 is along ˆr 21, which denotes repulsion, as it should be for
like charges |
1 | 242-245 | 3) are relevant:
·
Equation (1 3) is valid for any sign of q1 and q2 whether positive or
negative If q1 and q2 are of the same sign (either both positive or both
negative), F21 is along ˆr 21, which denotes repulsion, as it should be for
like charges If q1 and q2 are of opposite signs, F21 is along – ɵr 21(= ɵr 12),
which denotes attraction, as expected for unlike charges |
1 | 243-246 | 3) is valid for any sign of q1 and q2 whether positive or
negative If q1 and q2 are of the same sign (either both positive or both
negative), F21 is along ˆr 21, which denotes repulsion, as it should be for
like charges If q1 and q2 are of opposite signs, F21 is along – ɵr 21(= ɵr 12),
which denotes attraction, as expected for unlike charges Thus, we do
not have to write separate equations for the cases of like and unlike
charges |
1 | 244-247 | If q1 and q2 are of the same sign (either both positive or both
negative), F21 is along ˆr 21, which denotes repulsion, as it should be for
like charges If q1 and q2 are of opposite signs, F21 is along – ɵr 21(= ɵr 12),
which denotes attraction, as expected for unlike charges Thus, we do
not have to write separate equations for the cases of like and unlike
charges Equation (1 |
1 | 245-248 | If q1 and q2 are of opposite signs, F21 is along – ɵr 21(= ɵr 12),
which denotes attraction, as expected for unlike charges Thus, we do
not have to write separate equations for the cases of like and unlike
charges Equation (1 3) takes care of both cases correctly [Fig |
1 | 246-249 | Thus, we do
not have to write separate equations for the cases of like and unlike
charges Equation (1 3) takes care of both cases correctly [Fig 1 |
1 | 247-250 | Equation (1 3) takes care of both cases correctly [Fig 1 3(b)] |
1 | 248-251 | 3) takes care of both cases correctly [Fig 1 3(b)] FIGURE 1 |
1 | 249-252 | 1 3(b)] FIGURE 1 3 (a) Geometry and
(b) Forces between charges |
1 | 250-253 | 3(b)] FIGURE 1 3 (a) Geometry and
(b) Forces between charges Rationalised 2023-24
Electric Charges
and Fields
9
EXAMPLE 1 |
1 | 251-254 | FIGURE 1 3 (a) Geometry and
(b) Forces between charges Rationalised 2023-24
Electric Charges
and Fields
9
EXAMPLE 1 3
Interactive animation on Coulomb’s law:
http://webphysics |
1 | 252-255 | 3 (a) Geometry and
(b) Forces between charges Rationalised 2023-24
Electric Charges
and Fields
9
EXAMPLE 1 3
Interactive animation on Coulomb’s law:
http://webphysics davidson |
1 | 253-256 | Rationalised 2023-24
Electric Charges
and Fields
9
EXAMPLE 1 3
Interactive animation on Coulomb’s law:
http://webphysics davidson edu/physlet_resources/bu_semester2/menu_semester2 |
1 | 254-257 | 3
Interactive animation on Coulomb’s law:
http://webphysics davidson edu/physlet_resources/bu_semester2/menu_semester2 html
·
The force F12 on charge q1 due to charge q2, is obtained from Eq |
1 | 255-258 | davidson edu/physlet_resources/bu_semester2/menu_semester2 html
·
The force F12 on charge q1 due to charge q2, is obtained from Eq (1 |
1 | 256-259 | edu/physlet_resources/bu_semester2/menu_semester2 html
·
The force F12 on charge q1 due to charge q2, is obtained from Eq (1 3),
by simply interchanging 1 and 2, i |
1 | 257-260 | html
·
The force F12 on charge q1 due to charge q2, is obtained from Eq (1 3),
by simply interchanging 1 and 2, i e |
1 | 258-261 | (1 3),
by simply interchanging 1 and 2, i e ,
1
2
12
12
21
2
0
12
1
ˆ
4
ε
=
= −
π
F
r
F
q
q
r
Thus, Coulomb’s law agrees with the Newton’s third law |
1 | 259-262 | 3),
by simply interchanging 1 and 2, i e ,
1
2
12
12
21
2
0
12
1
ˆ
4
ε
=
= −
π
F
r
F
q
q
r
Thus, Coulomb’s law agrees with the Newton’s third law ·
Coulomb’s law [Eq |
1 | 260-263 | e ,
1
2
12
12
21
2
0
12
1
ˆ
4
ε
=
= −
π
F
r
F
q
q
r
Thus, Coulomb’s law agrees with the Newton’s third law ·
Coulomb’s law [Eq (1 |
1 | 261-264 | ,
1
2
12
12
21
2
0
12
1
ˆ
4
ε
=
= −
π
F
r
F
q
q
r
Thus, Coulomb’s law agrees with the Newton’s third law ·
Coulomb’s law [Eq (1 3)] gives the force between two charges q1 and
q2 in vacuum |
1 | 262-265 | ·
Coulomb’s law [Eq (1 3)] gives the force between two charges q1 and
q2 in vacuum If the charges are placed in matter or the intervening
space has matter, the situation gets complicated due to the presence
of charged constituents of matter |
1 | 263-266 | (1 3)] gives the force between two charges q1 and
q2 in vacuum If the charges are placed in matter or the intervening
space has matter, the situation gets complicated due to the presence
of charged constituents of matter We shall consider electrostatics in
matter in the next chapter |
1 | 264-267 | 3)] gives the force between two charges q1 and
q2 in vacuum If the charges are placed in matter or the intervening
space has matter, the situation gets complicated due to the presence
of charged constituents of matter We shall consider electrostatics in
matter in the next chapter Example 1 |
1 | 265-268 | If the charges are placed in matter or the intervening
space has matter, the situation gets complicated due to the presence
of charged constituents of matter We shall consider electrostatics in
matter in the next chapter Example 1 3 Coulomb’s law for electrostatic force between two point
charges and Newton’s law for gravitational force between two stationary
point masses, both have inverse-square dependence on the distance
between the charges and masses respectively |
1 | 266-269 | We shall consider electrostatics in
matter in the next chapter Example 1 3 Coulomb’s law for electrostatic force between two point
charges and Newton’s law for gravitational force between two stationary
point masses, both have inverse-square dependence on the distance
between the charges and masses respectively (a) Compare the strength
of these forces by determining the ratio of their magnitudes (i) for an
electron and a proton and (ii) for two protons |
1 | 267-270 | Example 1 3 Coulomb’s law for electrostatic force between two point
charges and Newton’s law for gravitational force between two stationary
point masses, both have inverse-square dependence on the distance
between the charges and masses respectively (a) Compare the strength
of these forces by determining the ratio of their magnitudes (i) for an
electron and a proton and (ii) for two protons (b) Estimate the
accelerations of electron and proton due to the electrical force of their
mutual attraction when they are 1 Å (= 10-10 m) apart |
1 | 268-271 | 3 Coulomb’s law for electrostatic force between two point
charges and Newton’s law for gravitational force between two stationary
point masses, both have inverse-square dependence on the distance
between the charges and masses respectively (a) Compare the strength
of these forces by determining the ratio of their magnitudes (i) for an
electron and a proton and (ii) for two protons (b) Estimate the
accelerations of electron and proton due to the electrical force of their
mutual attraction when they are 1 Å (= 10-10 m) apart (mp = 1 |
1 | 269-272 | (a) Compare the strength
of these forces by determining the ratio of their magnitudes (i) for an
electron and a proton and (ii) for two protons (b) Estimate the
accelerations of electron and proton due to the electrical force of their
mutual attraction when they are 1 Å (= 10-10 m) apart (mp = 1 67 ×
10–27 kg, me = 9 |
1 | 270-273 | (b) Estimate the
accelerations of electron and proton due to the electrical force of their
mutual attraction when they are 1 Å (= 10-10 m) apart (mp = 1 67 ×
10–27 kg, me = 9 11 × 10–31 kg)
Solution
(a) (i) The electric force between an electron and a proton at a distance
r apart is:
2
2
0
41
e
e
F
r
ε
= −
π
where the negative sign indicates that the force is attractive |
1 | 271-274 | (mp = 1 67 ×
10–27 kg, me = 9 11 × 10–31 kg)
Solution
(a) (i) The electric force between an electron and a proton at a distance
r apart is:
2
2
0
41
e
e
F
r
ε
= −
π
where the negative sign indicates that the force is attractive The
corresponding gravitational force (always attractive) is:
2
p
e
G
m
m
F
G
r
= −
where mp and me are the masses of a proton and an electron
respectively |
1 | 272-275 | 67 ×
10–27 kg, me = 9 11 × 10–31 kg)
Solution
(a) (i) The electric force between an electron and a proton at a distance
r apart is:
2
2
0
41
e
e
F
r
ε
= −
π
where the negative sign indicates that the force is attractive The
corresponding gravitational force (always attractive) is:
2
p
e
G
m
m
F
G
r
= −
where mp and me are the masses of a proton and an electron
respectively 2
39
0
2 |
1 | 273-276 | 11 × 10–31 kg)
Solution
(a) (i) The electric force between an electron and a proton at a distance
r apart is:
2
2
0
41
e
e
F
r
ε
= −
π
where the negative sign indicates that the force is attractive The
corresponding gravitational force (always attractive) is:
2
p
e
G
m
m
F
G
r
= −
where mp and me are the masses of a proton and an electron
respectively 2
39
0
2 4
10
4
e
G
p
e
F
e
F
εGm m
=
=
×
π
(ii) On similar lines, the ratio of the magnitudes of electric force
to the gravitational force between two protons at a distance r
apart is:
FF
e
Gm m
e
G
p
p
=
=
2
4πε0
1 |
1 | 274-277 | The
corresponding gravitational force (always attractive) is:
2
p
e
G
m
m
F
G
r
= −
where mp and me are the masses of a proton and an electron
respectively 2
39
0
2 4
10
4
e
G
p
e
F
e
F
εGm m
=
=
×
π
(ii) On similar lines, the ratio of the magnitudes of electric force
to the gravitational force between two protons at a distance r
apart is:
FF
e
Gm m
e
G
p
p
=
=
2
4πε0
1 3 × 1036
However, it may be mentioned here that the signs of the two forces
are different |
1 | 275-278 | 2
39
0
2 4
10
4
e
G
p
e
F
e
F
εGm m
=
=
×
π
(ii) On similar lines, the ratio of the magnitudes of electric force
to the gravitational force between two protons at a distance r
apart is:
FF
e
Gm m
e
G
p
p
=
=
2
4πε0
1 3 × 1036
However, it may be mentioned here that the signs of the two forces
are different For two protons, the gravitational force is attractive
in nature and the Coulomb force is repulsive |
1 | 276-279 | 4
10
4
e
G
p
e
F
e
F
εGm m
=
=
×
π
(ii) On similar lines, the ratio of the magnitudes of electric force
to the gravitational force between two protons at a distance r
apart is:
FF
e
Gm m
e
G
p
p
=
=
2
4πε0
1 3 × 1036
However, it may be mentioned here that the signs of the two forces
are different For two protons, the gravitational force is attractive
in nature and the Coulomb force is repulsive The actual values
of these forces between two protons inside a nucleus (distance
between two protons is ~ 10-15 m inside a nucleus) are Fe ~ 230 N,
whereas, FG ~ 1 |
1 | 277-280 | 3 × 1036
However, it may be mentioned here that the signs of the two forces
are different For two protons, the gravitational force is attractive
in nature and the Coulomb force is repulsive The actual values
of these forces between two protons inside a nucleus (distance
between two protons is ~ 10-15 m inside a nucleus) are Fe ~ 230 N,
whereas, FG ~ 1 9 × 10–34 N |
1 | 278-281 | For two protons, the gravitational force is attractive
in nature and the Coulomb force is repulsive The actual values
of these forces between two protons inside a nucleus (distance
between two protons is ~ 10-15 m inside a nucleus) are Fe ~ 230 N,
whereas, FG ~ 1 9 × 10–34 N The (dimensionless) ratio of the two forces shows that electrical
forces are enormously stronger than the gravitational forces |
1 | 279-282 | The actual values
of these forces between two protons inside a nucleus (distance
between two protons is ~ 10-15 m inside a nucleus) are Fe ~ 230 N,
whereas, FG ~ 1 9 × 10–34 N The (dimensionless) ratio of the two forces shows that electrical
forces are enormously stronger than the gravitational forces Rationalised 2023-24
10
Physics
(b) The electric force F exerted by a proton on an electron is same in
magnitude to the force exerted by an electron on a proton; however,
the masses of an electron and a proton are different |
1 | 280-283 | 9 × 10–34 N The (dimensionless) ratio of the two forces shows that electrical
forces are enormously stronger than the gravitational forces Rationalised 2023-24
10
Physics
(b) The electric force F exerted by a proton on an electron is same in
magnitude to the force exerted by an electron on a proton; however,
the masses of an electron and a proton are different Thus, the
magnitude of force is
|F| =
41
0
2
2
πε
re
= 8 |
1 | 281-284 | The (dimensionless) ratio of the two forces shows that electrical
forces are enormously stronger than the gravitational forces Rationalised 2023-24
10
Physics
(b) The electric force F exerted by a proton on an electron is same in
magnitude to the force exerted by an electron on a proton; however,
the masses of an electron and a proton are different Thus, the
magnitude of force is
|F| =
41
0
2
2
πε
re
= 8 987 × 109 Nm2/C2 × (1 |
1 | 282-285 | Rationalised 2023-24
10
Physics
(b) The electric force F exerted by a proton on an electron is same in
magnitude to the force exerted by an electron on a proton; however,
the masses of an electron and a proton are different Thus, the
magnitude of force is
|F| =
41
0
2
2
πε
re
= 8 987 × 109 Nm2/C2 × (1 6 ×10–19C)2 / (10–10m)2
= 2 |
1 | 283-286 | Thus, the
magnitude of force is
|F| =
41
0
2
2
πε
re
= 8 987 × 109 Nm2/C2 × (1 6 ×10–19C)2 / (10–10m)2
= 2 3 × 10–8 N
Using Newton’s second law of motion, F = ma, the acceleration
that an electron will undergo is
a = 2 |
1 | 284-287 | 987 × 109 Nm2/C2 × (1 6 ×10–19C)2 / (10–10m)2
= 2 3 × 10–8 N
Using Newton’s second law of motion, F = ma, the acceleration
that an electron will undergo is
a = 2 3×10–8 N / 9 |
1 | 285-288 | 6 ×10–19C)2 / (10–10m)2
= 2 3 × 10–8 N
Using Newton’s second law of motion, F = ma, the acceleration
that an electron will undergo is
a = 2 3×10–8 N / 9 11 ×10–31 kg = 2 |
1 | 286-289 | 3 × 10–8 N
Using Newton’s second law of motion, F = ma, the acceleration
that an electron will undergo is
a = 2 3×10–8 N / 9 11 ×10–31 kg = 2 5 × 1022 m/s2
Comparing this with the value of acceleration due to gravity, we
can conclude that the effect of gravitational field is negligible on
the motion of electron and it undergoes very large accelerations
under the action of Coulomb force due to a proton |
1 | 287-290 | 3×10–8 N / 9 11 ×10–31 kg = 2 5 × 1022 m/s2
Comparing this with the value of acceleration due to gravity, we
can conclude that the effect of gravitational field is negligible on
the motion of electron and it undergoes very large accelerations
under the action of Coulomb force due to a proton The value for acceleration of the proton is
2 |
1 | 288-291 | 11 ×10–31 kg = 2 5 × 1022 m/s2
Comparing this with the value of acceleration due to gravity, we
can conclude that the effect of gravitational field is negligible on
the motion of electron and it undergoes very large accelerations
under the action of Coulomb force due to a proton The value for acceleration of the proton is
2 3 × 10–8 N / 1 |
1 | 289-292 | 5 × 1022 m/s2
Comparing this with the value of acceleration due to gravity, we
can conclude that the effect of gravitational field is negligible on
the motion of electron and it undergoes very large accelerations
under the action of Coulomb force due to a proton The value for acceleration of the proton is
2 3 × 10–8 N / 1 67 × 10–27 kg = 1 |
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