Physics · Conductors and insulators, dielectrics and electric polarization
Two isolated metallic solid sphere of radius and are charged such that both of t
Two isolated metallic solid sphere of radius \( R \) and \( 2 R \) are charged such that both of these have same charge density
- A. the spheres are locted far away from each other and are connected by a thin conducting wire . the new charge density on the bigger sphere is A \( \cdot \frac{5 \sigma}{6} \)
- B. \( \frac{56 \sigma}{5} \)
- C. \( \frac{3 \sigma}{5} \)
- D. \( \frac{52 \sigma}{6} \)
Step-by-step solution
Initial charges: Q1 = σ·4πR², Q2 = σ·4π(2R)² = 16πσR², total Q = 20πσR². After connection, potentials equal: k Q1'/R = k Q2'/(2R) → Q2' = 2Q1'. Charge conservation: Q1' + 2Q1' = 20πσR² → Q1' = (20/3)πσR², Q2' = (40/3)πσR². New surface charge density on bigger sphere: σ2' = Q2'/(4π(2R)²) = (40/3 πσR²)/(16πR²) = (40)/(48)σ = (5/6)σ.
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