Calculations Using Coulomb's Law :
1. Determine the force between two charges, each of one coulomb when they are separated at one meter distance in air.
Solution: The magnitude of force between two charges is given by
F = (q1q2)/(4∏ϵoϵrd2) N
q1 = q2 = 1 coulomb
ϵo = absolute permittivity = 8.854 x 10-12 F/m
ϵr = 1 [Medium is air]
d= distance between the charges = 1m
F= (1×1)/4∏×1×1×1×8.854 x 10-12
F = 9 x 109 N
2. An electron and a proton are at a distance of 10-9 m from each other in free space. compute the force between them.
Solution : The charge on an electron, q1 = –1.6 × 10-19 C
and the charge on proton, q2 = + 1.6 × 10-19 C
The force between the two charges is given as,
F = (q1q2)/(4∏ϵoϵrd2) N
ϵo = absolute permittivity = 8.854 x 10-12 F/m
ϵr = 1
d = 10-9 m
F = ( –)1.6 × 10-19 C × (+ ) 1.6 × 10-19 C / 4∏×1×10-9 ×10-9 ×8.854 x 10-12
F = –23.04 × 10-11 N
The negative sign indicates that the force is of attraction .
For ease in calculations take the value of 1/ 4∏ϵo = 9 x 109
3. The magnitude of two charges is doubled and distance of their separation is also doubled. Find the coulomb's force between them.
Solution : F = Kq1q2/r2
F = Kq1'q2'/R2
q1' = 2q1
q2' = 2q2
R = 2r
= K. (2q1)(2q2)/4r2
= K. 4q1q2/ 4r2
= K. q1q2/ r2
= F.
Hence magnitude of coulomb's force will remain same.
Check your understanding with Multiple choice Questions:
1. The law that governs the force between electric charges is called
(a) Ampere's Law (b) Coulomb's Law
(c) Faraday's Law (d) Ohm's Law
2. Which one of the following is the unit of electric charge ?
(a) Coulomb (b) Newton
(c) Volt (d) Coulomb/Volt
3. When a conductor gets charged due too the mere presence of another body, the phenomenon is known as :
(a) friction (b) conduction
(c) induction (d) none of the above
4. Whenever induction takes place, the positive induced charges is equal to :
(a) inducing charge
(b) negative induced charge
(c) negative induced charge and also equal to the inducing charge
(d) none of the above
5. The distance between two charged bodies is halved, the force between them becomes :
(a) half (b) one fourth
(c) double (d) four times
6. The number of electrons in one coulomb of charge will be
(a) 5.46 × 1029
(b) 6.25 × 1018
(c) 1.6 × 1019
(d) 9 × 1011
7. The force between the electrons separated by a distance r varies as
(a) r2 (b) r -1
(c) r (d) r -2
8. The coulomb's force between two charges
(a) follow inverse square law
(b) it is conserved
(c) it is vector quantity
(d) it is additive in nature
9. Which of the following is not a property of electric charge ?
(a) It is discrete in nature
(b) It is conversed
(c) It is vector quantity
(d) It is addictive in nature
10. The magnitude of two charges is doubled and distance of their separation is also doubled. The electrostatic force between them will
(a) be halved (b) be doubled
(c) become four times (d) remains unchanged
11. Two charges are placed at a certain distance apart. A brass sheet is placed between them. The force between them will
(a) increase (b) decrease
(c) remains unchanged (d) none of the above
12 Two point charges placed at a distance r in air is 10 N. if they are in a medium of relative permittivity 4, the force between them will be :
(a) r (b) r/k
(c) r /√k (d) r √k
13. Two balls carrying charges of + 3 µc and – 3 µc attract each other with a force F. If charge + 3 µc is added to both, the force between the balls will be :
(a) 4F (b) 2F
(c) F (d) zero
14. Force between two charges, when placed in free space is 10 N. If they are in medium of relative permittivity 5, the force between them will be :
(a) 0.5 N (b) 2 N
(c) 20 N (d) 50 N
15. Force between two charges when placed in air is 10 N. If they are in a medium of relative permittivity 4, the force between them will be :
(a) 2 N (b) 2.5 N
(c) 0.4 N (d) 40 N
16. Two electrons are separated by distance 'r' mere and have a coulomb force equal to F. Two alpha particles separated by 2r meters will have force equal to
(a) 2 F (b) 3 F
(c) F/2 (d) F
17. The permittivity of the vacuum is:
(a) unity (b) more than one
(c) less than one but not zero (d) zero
18. If one of the two given charges is doubled and the distance between them is reduced to half, the coulomb force between them will increase by a factor of :
(a) 16 (b) 8
(c) 4 (d) 2
19. One coulomb is the point charge which when placed at one meter from an equal and similar point charge in vacuum repels it with a force :
(a) 9 x 109 dyne (b) 9 x 109 N
(c) 1 dyne (d) 1 N
20. The value of 4∏ϵo (in mks system) is :
(a) 9 x 109 (b) 1 / (9 x 109)
(c) 1 (d) 8.8 x 10-12
Answers:
1. b
2. a
3. c
4. c
5. d
6. b
7. d
8. a
9. c
10. d
11. a
12. c
13. d
14. b
15. b
16. d
17. c
18. d
19. b
20. b
1. Determine the force between two charges, each of one coulomb when they are separated at one meter distance in air.
Solution: The magnitude of force between two charges is given by
F = (q1q2)/(4∏ϵoϵrd2) N
q1 = q2 = 1 coulomb
ϵo = absolute permittivity = 8.854 x 10-12 F/m
ϵr = 1 [Medium is air]
d= distance between the charges = 1m
F= (1×1)/4∏×1×1×1×8.854 x 10-12
F = 9 x 109 N
2. An electron and a proton are at a distance of 10-9 m from each other in free space. compute the force between them.
Solution : The charge on an electron, q1 = –1.6 × 10-19 C
and the charge on proton, q2 = + 1.6 × 10-19 C
The force between the two charges is given as,
F = (q1q2)/(4∏ϵoϵrd2) N
ϵo = absolute permittivity = 8.854 x 10-12 F/m
ϵr = 1
d = 10-9 m
F = ( –)1.6 × 10-19 C × (+ ) 1.6 × 10-19 C / 4∏×1×10-9 ×10-9 ×8.854 x 10-12
F = –23.04 × 10-11 N
The negative sign indicates that the force is of attraction .
For ease in calculations take the value of 1/ 4∏ϵo = 9 x 109
3. The magnitude of two charges is doubled and distance of their separation is also doubled. Find the coulomb's force between them.
Solution : F = Kq1q2/r2
F = Kq1'q2'/R2
q1' = 2q1
q2' = 2q2
R = 2r
= K. (2q1)(2q2)/4r2
= K. 4q1q2/ 4r2
= K. q1q2/ r2
= F.
Hence magnitude of coulomb's force will remain same.
Check your understanding with Multiple choice Questions:
1. The law that governs the force between electric charges is called
(a) Ampere's Law (b) Coulomb's Law
(c) Faraday's Law (d) Ohm's Law
2. Which one of the following is the unit of electric charge ?
(a) Coulomb (b) Newton
(c) Volt (d) Coulomb/Volt
3. When a conductor gets charged due too the mere presence of another body, the phenomenon is known as :
(a) friction (b) conduction
(c) induction (d) none of the above
4. Whenever induction takes place, the positive induced charges is equal to :
(a) inducing charge
(b) negative induced charge
(c) negative induced charge and also equal to the inducing charge
(d) none of the above
5. The distance between two charged bodies is halved, the force between them becomes :
(a) half (b) one fourth
(c) double (d) four times
6. The number of electrons in one coulomb of charge will be
(a) 5.46 × 1029
(b) 6.25 × 1018
(c) 1.6 × 1019
(d) 9 × 1011
7. The force between the electrons separated by a distance r varies as
(a) r2 (b) r -1
(c) r (d) r -2
8. The coulomb's force between two charges
(a) follow inverse square law
(b) it is conserved
(c) it is vector quantity
(d) it is additive in nature
9. Which of the following is not a property of electric charge ?
(a) It is discrete in nature
(b) It is conversed
(c) It is vector quantity
(d) It is addictive in nature
10. The magnitude of two charges is doubled and distance of their separation is also doubled. The electrostatic force between them will
(a) be halved (b) be doubled
(c) become four times (d) remains unchanged
11. Two charges are placed at a certain distance apart. A brass sheet is placed between them. The force between them will
(a) increase (b) decrease
(c) remains unchanged (d) none of the above
12 Two point charges placed at a distance r in air is 10 N. if they are in a medium of relative permittivity 4, the force between them will be :
(a) r (b) r/k
(c) r /√k (d) r √k
13. Two balls carrying charges of + 3 µc and – 3 µc attract each other with a force F. If charge + 3 µc is added to both, the force between the balls will be :
(a) 4F (b) 2F
(c) F (d) zero
14. Force between two charges, when placed in free space is 10 N. If they are in medium of relative permittivity 5, the force between them will be :
(a) 0.5 N (b) 2 N
(c) 20 N (d) 50 N
15. Force between two charges when placed in air is 10 N. If they are in a medium of relative permittivity 4, the force between them will be :
(a) 2 N (b) 2.5 N
(c) 0.4 N (d) 40 N
16. Two electrons are separated by distance 'r' mere and have a coulomb force equal to F. Two alpha particles separated by 2r meters will have force equal to
(a) 2 F (b) 3 F
(c) F/2 (d) F
17. The permittivity of the vacuum is:
(a) unity (b) more than one
(c) less than one but not zero (d) zero
18. If one of the two given charges is doubled and the distance between them is reduced to half, the coulomb force between them will increase by a factor of :
(a) 16 (b) 8
(c) 4 (d) 2
19. One coulomb is the point charge which when placed at one meter from an equal and similar point charge in vacuum repels it with a force :
(a) 9 x 109 dyne (b) 9 x 109 N
(c) 1 dyne (d) 1 N
20. The value of 4∏ϵo (in mks system) is :
(a) 9 x 109 (b) 1 / (9 x 109)
(c) 1 (d) 8.8 x 10-12
Answers:
1. b
2. a
3. c
4. c
5. d
6. b
7. d
8. a
9. c
10. d
11. a
12. c
13. d
14. b
15. b
16. d
17. c
18. d
19. b
20. b
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