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Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere 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. I What were the initial charges on the sphere?
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?Two identical conducting spheres ( of negligible radius) I having cha...
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?Two identical conducting spheres ( of negligible radius) I having cha...
Initial Charges Calculation:
- Let the initial charges on the spheres be Q1 and Q2.
- According to Coulomb's law, the force between the spheres is given by:
F = k * |Q1 * Q2| / r^2, where k is the Coulomb constant, r is the distance between the spheres.
- Given F = 0.108 N, Q1 = -Q2, and r = 0.5 m, we can calculate the initial charges.

Step 1: Calculating the Initial Charges:
- Using the formula F = k * |Q1 * Q2| / r^2, we get:
0.108 = (9 x 10^9) * |Q1^2| / (0.5)^2
- Solving for Q1, we get Q1 = ±1.296 x 10^-6 C.

Step 2: Repulsion Force Calculation:
- When the spheres are connected by a wire, charge flows until they reach equilibrium.
- At equilibrium, the charges on the spheres are such that they repel each other with a force of 0.036 N.
- This means that the charges will be redistributed until the repulsive force balances out the attractive force.

Step 3: Calculating the Final Charges:
- Using the formula F = k * |Q1 * Q2| / r^2, we get:
0.036 = (9 x 10^9) * |Q1 * Q2| / (0.5)^2
- Since Q1 = -Q2, we substitute Q2 = -Q1 into the equation and solve for Q1.
- Solving for Q1, we get Q1 = ±4.32 x 10^-7 C.

Conclusion:
- The initial charges on the spheres were ±1.296 x 10^-6 C, with one sphere having positive charge and the other having an equal magnitude of negative charge.
- After charge redistribution, the final charges on the spheres were ±4.32 x 10^-7 C, resulting in repulsion with a force of 0.036 N.
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?Two identical conducting spheres ( of negligible radius) I having charge of of opposite sign, I attract each other with a force of 0.108 N when separated by 0.5 meter. The sphere 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. I What were the initial charges on the sphere?
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