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Two identical conducting spheres (of negligible radius), having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres are connected by a conducting wire, which is then removed (when charge stops flowing), and thereafter repel each other with a force of 0.036 N keeping the distance same. What were the initial charges on the spheres?
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Two identical conducting spheres (of negligible radius), having charge...
Initial setup:
- Two identical conducting spheres with negligible radius
- Charges of opposite sign
- Attract each other with a force of 0.108 N
- Separated by 0.5 meter

After connecting and disconnecting:
- Connected by a conducting wire and then removed
- Repel each other with a force of 0.036 N
- Distance between spheres remains 0.5 meter

To find: Initial charges on the spheres

Solution:
Step 1: Calculate the initial force between the spheres
- Using Coulomb's Law: F = (k*q1*q2)/r^2, where k is Coulomb's constant, q1 and q2 are charges on the spheres, and r is the distance between them
- Rearranging the equation: q1*q2 = (F*r^2)/k
- Substituting values: q1*q2 = (0.108 N)*(0.5 m)^2/(9*10^9 N m^2/C^2) = 1.2*10^-9 C^2

Step 2: Calculate the final charges on the spheres
- After connecting the spheres, the charges will redistribute themselves to reach equilibrium
- Since the spheres are identical, they will have equal charges after redistribution
- Let the final charge on each sphere be qf
- Using the principle of conservation of charge: q1 + q2 = 2*qf
- Substituting q1*q2 from step 1: (qf)^2 = (1.2*10^-9 C^2)/4 = 0.3*10^-9 C^2
- Taking the square root: qf = 0.547 nC (nanoCoulombs)

Step 3: Calculate the initial charges on the spheres
- Let the initial charge on one sphere be qi
- The other sphere will have charge -qi (opposite sign)
- Using the principle of conservation of charge: qi - qi = 2*qf
- Substituting values: qi = qf = 0.547 nC

Final answer: The initial charges on the spheres were 0.547 nC, with one sphere having charge +0.547 nC and the other having charge -0.547 nC.
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Two identical conducting spheres (of negligible radius), having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres are connected by a conducting wire, which is then removed (when charge stops flowing), and thereafter repel each other with a force of 0.036 N keeping the distance same. What were the initial charges on the spheres?
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Two identical conducting spheres (of negligible radius), having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres are connected by a conducting wire, which is then removed (when charge stops flowing), and thereafter repel each other with a force of 0.036 N keeping the distance same. What were the initial charges on the spheres? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two identical conducting spheres (of negligible radius), having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres are connected by a conducting wire, which is then removed (when charge stops flowing), and thereafter repel each other with a force of 0.036 N keeping the distance same. What were the initial charges on the spheres? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical conducting spheres (of negligible radius), having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres are connected by a conducting wire, which is then removed (when charge stops flowing), and thereafter repel each other with a force of 0.036 N keeping the distance same. What were the initial charges on the spheres?.
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