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2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is?
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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.
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.
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2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is?
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2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is?.
2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 metallic spheres of radii in a ratio 3:2are charged if they are connected by a conducting wire.The ratio of electric potential of sphere long time after connection is?.
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