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Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?
A. -(3+✓8) only. B.-3+✓8 only.
C.both A and B. D.+✓3.?
A. -(3+✓8) only. B.-3+✓8 only.
C.both A and B. D.+✓3.?
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Two identical conducting spheres carrying different charges attract ea...
Given 2 identical conducting spheres carrying different charges attract each other with force F when placed in air medium 'd' apart...;Now; the sphere are brought in to contact and then taken to their original position Now, the 2 spheres repel each other with force F...;We have to find ratio b/w initial charges....;Since 2 charges attract; they will be opposite in sign ie. q1&−q2...Force =4πr21d2q1q2..After touching, charges on each will be2q1−q2....New force is: f=4πε01(2q1−q2)2/d2.....since both the force are same; so on solving by quadratic equation;4πϵo1d2q1q2=4πε014d2(q1−q2)2..⇒4q1q2=q12+q22−2q1q2⇒q12+q22−6q1q2=0...so; dividing by q1q2; ..we get;q2q1+q1q2=6..so; we get q2q1=(3+8)or(−3+8)..so the answer is option (c)...
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Two identical conducting spheres carrying different charges attract ea...
Given: Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart.
To find: The ratio between initial charges on the spheres.
Let the initial charges on each sphere be q1 and q2, respectively. Since the spheres are identical, the charges will be equal after they are brought into contact and then taken to their original positions. Let the final charge on each sphere be q.
Attractive Force between two charged spheres:
The force of attraction between two charged spheres is given by Coulomb's law as:
F = (1/4πε0) * (q1*q2/d^2)
where ε0 is the permittivity of free space.
After the spheres are brought into contact, the charges on each sphere will be equal and given by:
q = (q1 + q2)/2
Repulsive Force between two charged spheres:
The force of repulsion between two charged spheres is given by Coulomb's law as:
F' = (1/4πε0) * (q^2/d^2)
It is given that F' = F.
Substituting the values of F and F', we get:
(1/4πε0) * (q1*q2/d^2) = (1/4πε0) * (q^2/d^2)
q1*q2 = q^2
q1/q2 = q/q1
q1/q2 = (q1+q2)/2q1
q1/q2 = 1 + q2/2q1
q1/q2 - 1 = q2/2q1
2q1(q1/q2 - 1) = q2
2q1/q2 * (q1 - q2) = -q2
q1/q2 = -q2/2q1 + 1/2
q1/q2 = (-1/2) * (√3)^2 + 1/2 (as q1/q2 = -3√8 or -3√8)
q1/q2 = 1/2
Therefore, the ratio between initial charges on the spheres is 1:2. Answer: D. √3.
To find: The ratio between initial charges on the spheres.
Let the initial charges on each sphere be q1 and q2, respectively. Since the spheres are identical, the charges will be equal after they are brought into contact and then taken to their original positions. Let the final charge on each sphere be q.
Attractive Force between two charged spheres:
The force of attraction between two charged spheres is given by Coulomb's law as:
F = (1/4πε0) * (q1*q2/d^2)
where ε0 is the permittivity of free space.
After the spheres are brought into contact, the charges on each sphere will be equal and given by:
q = (q1 + q2)/2
Repulsive Force between two charged spheres:
The force of repulsion between two charged spheres is given by Coulomb's law as:
F' = (1/4πε0) * (q^2/d^2)
It is given that F' = F.
Substituting the values of F and F', we get:
(1/4πε0) * (q1*q2/d^2) = (1/4πε0) * (q^2/d^2)
q1*q2 = q^2
q1/q2 = q/q1
q1/q2 = (q1+q2)/2q1
q1/q2 = 1 + q2/2q1
q1/q2 - 1 = q2/2q1
2q1(q1/q2 - 1) = q2
2q1/q2 * (q1 - q2) = -q2
q1/q2 = -q2/2q1 + 1/2
q1/q2 = (-1/2) * (√3)^2 + 1/2 (as q1/q2 = -3√8 or -3√8)
q1/q2 = 1/2
Therefore, the ratio between initial charges on the spheres is 1:2. Answer: D. √3.
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Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.?
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Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.?.
Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions.now the two spheres repel each other with a force whole magnitude equal to that of the initial attractive force.the ratio between initial charges on the spheres is?A. -(3+✓8) only. B.-3+✓8 only.C.both A and B. D.+✓3.?.
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