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Question
Two metal spheres having charge densities 5μC/m2 and -2μC/m2 with radii 2mm and 1mm respectively are kept in a hypothetical closed surface. Calculate total normal electric induction over the closed surface.
Solution
σ1 = 5 μC/m2
σ2 = -2 μC/m2
r1 = 2 mm
r2 = 1 mm
q1 = σ14π r12
q2 = σ24π r22
T.N.E.I. = q1 + q2
∴T.N.E.I. = 4π(σ1r12 + σ2r22)
∴T.N.E.I. = 4π(5 × 10-6 × 4 × 10-6 + (−2) × 10-6 × 1 × 10-6)
∴T.N.E.I. = 72π × 10-12 C
∴T.N.E.I. = 226.08 × 10-12 C
Hence, the total normal electric induction over the closed surface is 226.08 × 10-12 C.
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