2 metallic spheres of radii in a ratio 3:2are charged if they are conn...
Explanation:
1. Initial Charge Distribution:
- Initially, the two metallic spheres have charges q1 and q2 where q1 and q2 are directly proportional to the radii r1 and r2 of the spheres.
- Given that the radii are in the ratio 3:2, let the charges on the spheres be 3q and 2q initially.
2. Electric Potential Calculation:
- The electric potential of a sphere is given by V = kq/r, where k is the electrostatic constant, q is the charge, and r is the radius.
- The potential difference between the spheres before connection is V1 = k(3q)/r1 and V2 = k(2q)/r2.
3. Equilibration of Charges:
- When the two spheres are connected by a conducting wire, charge will flow from the sphere with higher potential to the one with lower potential.
- This process will continue until the potentials of both spheres become equal.
4. Final Charge Distribution:
- Let the final charges on the spheres be Q1 and Q2 after equilibration.
- Since the total charge is conserved, Q1 + Q2 = 5q (initial total charge).
- The final potential difference between the spheres is V = kQ1/r1 = kQ2/r2.
5. Final Electric Potential Ratio:
- Since V = kQ1/r1 = kQ2/r2, we have Q1/r1 = Q2/r2.
- Therefore, the ratio of electric potentials after a long time is V1/V2 = Q1/r1 / Q2/r2 = r2/r1 = 2/3.
Thus, the ratio of electric potentials of the spheres long time after connection is 2:3.
2 metallic spheres of radii in a ratio 3:2are charged if they are conn...
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