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Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.?
Verified Answer
Two identical spheres having charges of opposite sign attract each oth...
F1 = 0.108 N
r = 0.5 m
F2 = 0.036 N
Let charges on the spheres be q1 and q2 respectively.
Charges after connection gets redistributed in the spheres, so be q in each of the spheres
From conservation of charge
q1 + q2 = 2q ---1.
Again
F1 = k q1q2/r^2 ---2
F2 = k q^2/r^2 ----3
=> 0.036 = 9x10^9xq^2/(0.5)^2
=> q^2 = 0.036x(0.5)^2/9x10^9
=> q^2 = 0.036/(4x9x10^9)
=> q^2 = 1x10^-12
=> q = 1x10^-6 C ---4
From 2 and 3
F1/F2 = q1q2/q^2
=> 3 = q1q2/q^2
=> 3q^2 = q1q2
=> q1q2 = 3q^2
Again,
(q1 – q2)^2 = (q1 + q2)^2 – 4q1q2
= (2q)^2 – 3q^2/ r^2
= q^2/ r^2
By 4
(q1 – q2) = q/r
= 1x10^-6/ 0.5
= 2x10^-6 ---5
From 1 and 4.
q1 + q2 = 4x10^-6 ---6.
Adding 5 and 6
q1 = 3x10^-6
= 3μC
Subtracting 5 from 6
q2 = 1x10^-6
= 1μC
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Two identical spheres having charges of opposite sign attract each oth...
Initial Attraction Force:
- Two identical spheres with charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m.
- Let's assume that the charges on the spheres are q1 and q2, and they have opposite signs.
Using Coulomb's Law, the formula to calculate the force between two charged objects is:
F = k * |q1 * q2| / r^2
- F is the force between the spheres,
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
- q1 and q2 are the charges on the spheres,
- r is the separation distance between the spheres.
- In this case, the force of attraction is given as 0.108N, and the separation distance is 0.5m.
- We can rewrite Coulomb's Law as:
0.108 = (9 x 10^9) * |q1 * q2| / (0.5^2)
- Since the spheres have identical charges with opposite signs, we can simplify the equation to:
0.108 = (9 x 10^9) * q^2 / (0.5^2)
- Solving for q^2:
q^2 = (0.108 * 0.5^2) / (9 x 10^9)
q^2 = 3 x 10^-11
- Taking the square root of both sides:
q = ± √(3 x 10^-11)
- Since the spheres have opposite charges, we can assign one charge as positive and the other as negative.
- Therefore, the initial charges on the spheres are ± √(3 x 10^-11) Coulombs.
Repulsion Force after Connection:
- The spheres are connected by a conducting wire and then removed, and thereafter they repel each other with a force of 0.036N.
- When the spheres are connected by a conducting wire, they will share their charges, equalizing them.
- Let's assume that the final charges on the spheres after connection are Q1 and Q2.
- Since the spheres are identical, the charges will be equal, so Q1 = Q2 = Q.
Using Coulomb's Law again, we can calculate the repulsion force:
F = k * |Q * Q| / r^2
- In this case, the force of repulsion is given as 0.036N, and the separation distance is still 0.5m.
0.036 = (9 x 10^9) * Q^2 / (0.5^2)
- Solving for Q^2:
Q^2 = (0.036 * 0.5^2) / (9 x 10^9)
Q^2 = 2 x 10^-12
- Taking the square root of both sides:
Q = ± √(2 x 10^-12)
- Since the spheres have opposite charges, we can assign one charge as positive and the other as negative.
- Therefore, the final charges on the spheres after connection are ± √(2 x 10^-12) Coulombs.
In conclusion, the initial charges on the spheres are ± √(3 x 10^-11) Coulombs, and the final charges after connection are ± √(2
- Two identical spheres with charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m.
- Let's assume that the charges on the spheres are q1 and q2, and they have opposite signs.
Using Coulomb's Law, the formula to calculate the force between two charged objects is:
F = k * |q1 * q2| / r^2
- F is the force between the spheres,
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
- q1 and q2 are the charges on the spheres,
- r is the separation distance between the spheres.
- In this case, the force of attraction is given as 0.108N, and the separation distance is 0.5m.
- We can rewrite Coulomb's Law as:
0.108 = (9 x 10^9) * |q1 * q2| / (0.5^2)
- Since the spheres have identical charges with opposite signs, we can simplify the equation to:
0.108 = (9 x 10^9) * q^2 / (0.5^2)
- Solving for q^2:
q^2 = (0.108 * 0.5^2) / (9 x 10^9)
q^2 = 3 x 10^-11
- Taking the square root of both sides:
q = ± √(3 x 10^-11)
- Since the spheres have opposite charges, we can assign one charge as positive and the other as negative.
- Therefore, the initial charges on the spheres are ± √(3 x 10^-11) Coulombs.
Repulsion Force after Connection:
- The spheres are connected by a conducting wire and then removed, and thereafter they repel each other with a force of 0.036N.
- When the spheres are connected by a conducting wire, they will share their charges, equalizing them.
- Let's assume that the final charges on the spheres after connection are Q1 and Q2.
- Since the spheres are identical, the charges will be equal, so Q1 = Q2 = Q.
Using Coulomb's Law again, we can calculate the repulsion force:
F = k * |Q * Q| / r^2
- In this case, the force of repulsion is given as 0.036N, and the separation distance is still 0.5m.
0.036 = (9 x 10^9) * Q^2 / (0.5^2)
- Solving for Q^2:
Q^2 = (0.036 * 0.5^2) / (9 x 10^9)
Q^2 = 2 x 10^-12
- Taking the square root of both sides:
Q = ± √(2 x 10^-12)
- Since the spheres have opposite charges, we can assign one charge as positive and the other as negative.
- Therefore, the final charges on the spheres after connection are ± √(2 x 10^-12) Coulombs.
In conclusion, the initial charges on the spheres are ± √(3 x 10^-11) Coulombs, and the final charges after connection are ± √(2
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Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.?
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Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.? 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 Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.?.
Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.? 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 Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by conducting wire, which then removed, and thereafter they repel each other with a force of 0.036N. What were the initial charges on the spheres.?.
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