Question

two metallic spheres of radii R1 and R2 are charged. now they are brought into contact with help of conducting wire and than are separated from each other. if electric field at their surfaces are E1 and E2 , then E1/E2=.......​

Answer 1

1. Question⇒   two metallic spheres of radii R1 and R2 are charged. now they are brought into contact with help of conducting wire and than are separated from each other. if electric field at their surfaces are E1 and E2 , then E1/E2=.......​

Explanation:

• Two charged conducting sphere of radii r₁ and r₂ respectively connected to each other by a wire.
• so, capacitance of 1st sphere , C₁ = 4πε₀r₁
• capacitance of 2nd sphere , C₂ = 4πε₀r₂
• After connecting , transfer of charge from higher potential sphere to lower potential sphere and finally, potential of both sphere will be equal .Let final potential is V
• Now, charge at 1st sphere, Q₁= C₁V = 4πε₀r₁V
• charge at 2nd sphere ,Q₂ = C₂V = 4πε₀r₂V
• so, ratio of charge = Q₁/Q₂= 4πε₀r₁V/4πε₀r₂V = r₁/r₂ -------(1)
• Now, ratio of electric field = E₁/E₂ = KQ₁/r₁²/KQ₂/r₂² = Q₁r₂²/Q₂r₁²
• E₁/E₂ = {Q₁/Q₂}{r₂²/r₁²}
• Put equation (1)
• E₁/E₂ = r₂/r₁

• Hence, ratio of electric field is r₂ : r₁