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Calculate Total Normal Electric Induction Over the Closed Surface. - Physics

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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.

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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.

Concept: Inductance and Capacitance
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