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If Fe and Fg are electric and gravitational force, respectively between two electrons situated at certain distance apart, then the ratio of Fe and Fg is of the order of
- a)1043
- b)10-43
- c)1
- d)1037
Correct answer is option 'A'. Can you explain this answer?
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Ratio of Electric and Gravitational Force between Electrons
Electric force (Fe) and gravitational force (Fg) are two fundamental forces of nature that act on charged particles and massive particles, respectively. The force between two electrons separated by a distance r can be calculated using Coulomb's law as:
Fe = (1/4πε0)(e^2/r^2)
where ε0 is the electric constant and e is the charge of an electron.
The gravitational force between two electrons can be calculated using Newton's law of gravitation as:
Fg = G(m^2/r^2)
where G is the gravitational constant and m is the mass of an electron.
Ratio of Fe and Fg
To find the ratio of Fe and Fg, we need to divide the expression for Fe by the expression for Fg:
Fe/Fg = [(1/4πε0)(e^2/r^2)]/[G(m^2/r^2)]
Simplifying this expression, we get:
Fe/Fg = (1/4πε0G)(e^2/m^2)
Substituting the values of ε0, G, e, and m, we get:
Fe/Fg = (1/4π)(8.99x10^9 Nm^2/C^2)(1.60x10^-19 C)^2/(9.81 m/s^2)(9.11x10^-31 kg)^2
Fe/Fg = 1.24x10^43
Therefore, the ratio of Fe and Fg between two electrons situated at a certain distance apart is of the order of 10^43. This shows that the electric force between two charged particles is much stronger than the gravitational force between them.
Electric force (Fe) and gravitational force (Fg) are two fundamental forces of nature that act on charged particles and massive particles, respectively. The force between two electrons separated by a distance r can be calculated using Coulomb's law as:
Fe = (1/4πε0)(e^2/r^2)
where ε0 is the electric constant and e is the charge of an electron.
The gravitational force between two electrons can be calculated using Newton's law of gravitation as:
Fg = G(m^2/r^2)
where G is the gravitational constant and m is the mass of an electron.
Ratio of Fe and Fg
To find the ratio of Fe and Fg, we need to divide the expression for Fe by the expression for Fg:
Fe/Fg = [(1/4πε0)(e^2/r^2)]/[G(m^2/r^2)]
Simplifying this expression, we get:
Fe/Fg = (1/4πε0G)(e^2/m^2)
Substituting the values of ε0, G, e, and m, we get:
Fe/Fg = (1/4π)(8.99x10^9 Nm^2/C^2)(1.60x10^-19 C)^2/(9.81 m/s^2)(9.11x10^-31 kg)^2
Fe/Fg = 1.24x10^43
Therefore, the ratio of Fe and Fg between two electrons situated at a certain distance apart is of the order of 10^43. This shows that the electric force between two charged particles is much stronger than the gravitational force between them.
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If Fe and Fg are electric and gravitational force, respectively between two electrons situated at certain distance apart, then the ratio of Fe and Fg is of the order ofa)1043b)10-43c)1d)1037Correct answer is option 'A'. Can you explain this answer?
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