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Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is?
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Two isolated metallic solid spheres of radii R and 2R are charged such...
Given:
- Two isolated metallic solid spheres of radii R and 2R
- Both spheres have the same charge density σ
To Find:
- The new charge density σ' after the spheres are connected by a thin conducting wire
Explanation:
Step 1: Charge on each sphere
- The charge on a sphere can be calculated using the formula Q = 4πR²σ, where Q is the charge and R is the radius of the sphere.
- So, the charge on the smaller sphere is Q1 = 4πR²σ and the charge on the larger sphere is Q2 = 4π(2R)²σ = 16πR²σ
Step 2: Total charge before connecting
- The total charge before connecting the spheres is the sum of the charges on each sphere.
- So, the total charge before connecting is Q_total = Q1 + Q2 = 4πR²σ + 16πR²σ = 20πR²σ
Step 3: Total charge after connecting
- When the spheres are connected by a conducting wire, the charges on the spheres redistribute until they reach a state of equilibrium.
- In this state, the charges on the spheres will be equal.
- Let the charge on each sphere after connecting be Q_final.
- So, Q_final = Q_total/2 = 20πR²σ/2 = 10πR²σ
Step 4: Charge density after connecting
- The charge density of a sphere can be calculated using the formula σ = Q/(4πR²), where Q is the charge and R is the radius of the sphere.
- So, the charge density of the larger sphere after connecting is σ' = Q_final/(4π(2R)²) = 10πR²σ/(4π(2R)²) = 10σ/4 = 2.5σ
Step 5: Ratio of σ' to σ
- The ratio of σ' to σ is σ'/σ = 2.5σ/σ = 2.5
Final Answer:
- The ratio of σ' to σ is 2.5
- Two isolated metallic solid spheres of radii R and 2R
- Both spheres have the same charge density σ
To Find:
- The new charge density σ' after the spheres are connected by a thin conducting wire
Explanation:
Step 1: Charge on each sphere
- The charge on a sphere can be calculated using the formula Q = 4πR²σ, where Q is the charge and R is the radius of the sphere.
- So, the charge on the smaller sphere is Q1 = 4πR²σ and the charge on the larger sphere is Q2 = 4π(2R)²σ = 16πR²σ
Step 2: Total charge before connecting
- The total charge before connecting the spheres is the sum of the charges on each sphere.
- So, the total charge before connecting is Q_total = Q1 + Q2 = 4πR²σ + 16πR²σ = 20πR²σ
Step 3: Total charge after connecting
- When the spheres are connected by a conducting wire, the charges on the spheres redistribute until they reach a state of equilibrium.
- In this state, the charges on the spheres will be equal.
- Let the charge on each sphere after connecting be Q_final.
- So, Q_final = Q_total/2 = 20πR²σ/2 = 10πR²σ
Step 4: Charge density after connecting
- The charge density of a sphere can be calculated using the formula σ = Q/(4πR²), where Q is the charge and R is the radius of the sphere.
- So, the charge density of the larger sphere after connecting is σ' = Q_final/(4π(2R)²) = 10πR²σ/(4π(2R)²) = 10σ/4 = 2.5σ
Step 5: Ratio of σ' to σ
- The ratio of σ' to σ is σ'/σ = 2.5σ/σ = 2.5
Final Answer:
- The ratio of σ' to σ is 2.5
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Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is?
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Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is?.
Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density if the bigger sphere is σ '. The ratio of σ '/ σ is?.
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