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There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is 4.8 x 105 O 6.1 x 10² O2.8 x 106 9.3 × 1013?
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There are two small uncharged spheres placed at a distance of 1 m from...
Solution:
Given: Two small uncharged spheres placed at a distance of 1 m from each other, Force between the spheres after transfer of N electrons is measured to be equal to 2 Newton.
To find: Value of N.
Step 1: Understanding the concept
When two uncharged spheres are brought in contact and separated, they acquire equal and opposite charges due to the transfer of electrons. The force between them is given by Coulomb's law,
F = k (q1 x q2)/r²
where k is Coulomb's constant, q1 and q2 are charges on the spheres and r is the distance between them.
Step 2: Calculation of initial force
As the spheres are initially uncharged, the initial force between them is zero.
F(initial) = 0
Step 3: Calculation of final force
After N electrons are transferred from one sphere to another, the charges on the spheres become q and -q respectively. The force between them is given by,
F(final) = k (q²/r²)
where q = Ne (e is the charge on an electron)
F(final) = k (N²e²/r²)
F(final) = k (N² x (1.6 x 10^-19)^2/1^2)
F(final) = k (2.56 x 10^-37 x N²)
Step 4: Calculation of N
Given, F(final) = 2 N
2 = k (2.56 x 10^-37 x N²)
N² = (2/ k) x (1/2.56 x 10^-37)
N² = 7.8125 x 10^37
N = √(7.8125 x 10^37)
N = 2.8 x 10^18
Therefore, the value of N is 2.8 x 10^18.
Conclusion:
The value of N is 2.8 x 10^18. This is because the force between the spheres is directly proportional to the square of the charge on the spheres. When N electrons are transferred from one sphere to another, the charge on the spheres becomes q and -q respectively, resulting in a force between them that is proportional to N². By equating the final force to the given value of 2 Newton, we can calculate the value of N.
Given: Two small uncharged spheres placed at a distance of 1 m from each other, Force between the spheres after transfer of N electrons is measured to be equal to 2 Newton.
To find: Value of N.
Step 1: Understanding the concept
When two uncharged spheres are brought in contact and separated, they acquire equal and opposite charges due to the transfer of electrons. The force between them is given by Coulomb's law,
F = k (q1 x q2)/r²
where k is Coulomb's constant, q1 and q2 are charges on the spheres and r is the distance between them.
Step 2: Calculation of initial force
As the spheres are initially uncharged, the initial force between them is zero.
F(initial) = 0
Step 3: Calculation of final force
After N electrons are transferred from one sphere to another, the charges on the spheres become q and -q respectively. The force between them is given by,
F(final) = k (q²/r²)
where q = Ne (e is the charge on an electron)
F(final) = k (N²e²/r²)
F(final) = k (N² x (1.6 x 10^-19)^2/1^2)
F(final) = k (2.56 x 10^-37 x N²)
Step 4: Calculation of N
Given, F(final) = 2 N
2 = k (2.56 x 10^-37 x N²)
N² = (2/ k) x (1/2.56 x 10^-37)
N² = 7.8125 x 10^37
N = √(7.8125 x 10^37)
N = 2.8 x 10^18
Therefore, the value of N is 2.8 x 10^18.
Conclusion:
The value of N is 2.8 x 10^18. This is because the force between the spheres is directly proportional to the square of the charge on the spheres. When N electrons are transferred from one sphere to another, the charge on the spheres becomes q and -q respectively, resulting in a force between them that is proportional to N². By equating the final force to the given value of 2 Newton, we can calculate the value of N.
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There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is 4.8 x 105 O 6.1 x 10² O2.8 x 106 9.3 × 1013?
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There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is 4.8 x 105 O 6.1 x 10² O2.8 x 106 9.3 × 1013? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is 4.8 x 105 O 6.1 x 10² O2.8 x 106 9.3 × 1013? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is 4.8 x 105 O 6.1 x 10² O2.8 x 106 9.3 × 1013?.
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