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Two identical small conducting spheres having charge of opposite sign attract each other with a force of 0.108N when separated by 0.5 m, the spheres are connected by a conducting wire which is then removed and thereafter, the repel each other with the force of 0.036N.The initial charges on the sphere are?
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Two identical small conducting spheres having charge of opposite sign ...
Given Data:
- Force of attraction between spheres: 0.108N
- Separation between spheres: 0.5m
- Force of repulsion between spheres: 0.036N

Explanation:

Calculation of Initial Charges:
- The force of attraction between the spheres can be calculated using Coulomb's law: \( F = k \frac{q^2}{r^2} \), where k is the Coulomb constant.
- Substituting the given values, we get: \( 0.108 = k \frac{q^2}{(0.5)^2} \).
- Similarly, the force of repulsion can be calculated using the same formula.
- Substituting the given values, we get: \( 0.036 = k \frac{q^2}{(0.5)^2} \).

Solving for Initial Charges:
- By equating the two equations, we can solve for the initial charges on the spheres.
- \( k \frac{q_1^2}{(0.5)^2} = k \frac{q_2^2}{(0.5)^2} \).
- This simplifies to: \( q_1^2 = q_2^2 \).
- Since the charges are of opposite sign, we have: \( q_1 = -q_2 \).
- Substituting this into one of the equations, we can solve for the initial charges.

Final Answer:
- The initial charges on the spheres can be calculated using the above method.
- The charges will be such that the spheres attract each other with 0.108N force when separated by 0.5m and repel each other with 0.036N force after being connected by a conducting wire.
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Two identical small conducting spheres having charge of opposite sign attract each other with a force of 0.108N when separated by 0.5 m, the spheres are connected by a conducting wire which is then removed and thereafter, the repel each other with the force of 0.036N.The initial charges on the sphere are?
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