two sphere o radii 2cm and 4cm are charged equally, then the ratio of charge density on the surface of the sphere will be
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We know that,
Surface Charge Density = Charge/Surface Area
''Let the charge distributed on each sphere is q.''
Case I ⇒ For the Sphere of Radius 2 cm.
Surface Charge Density(σ₁) = q/4πr²
= q/4π(2)²
= q/4π(4)
Case II ⇒ For the Sphere of Radius 4 cm.
Surface Charge Density(σ₂) = q/4πr²
= q/4π(4)²
= q/4π(16)
Thus, σ₁/σ₂ = 16/4
∴ σ₁/σ₂ = 4/1
∴ σ₁ : σ₂ = 4 : 1
Hence, Option (2). is Correct.
Hope it helps.
Answered by
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Answer:
Case I ⇒ For the Sphere of Radius 2 cm.
Surface Charge Density(σ₁) = q/4πr²
= q/4π(2)²
= q/4π(4)
Case II ⇒ For the Sphere of Radius 4 cm.
Surface Charge Density(σ₂) = q/4πr²
= q/4π(4)²
= q/4π(16)
Thus, σ₁/σ₂ = 16/4
∴ σ₁/σ₂ = 4/1
∴ σ₁ : σ₂ = 4 : 1
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