A metal sphere with 1 m radius and a surface charge density

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A metal sphere with 1 m radius and a surface charge density of 10 coulomb/m2 is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is—

1. 40 π coulombs
2. 10 π coulombs
3. 5 π coulombs
4. None of these

Correct Option: D

We have total charge enclosed by cube
q_total = A. σ = 4 σr² × 10 = 40 σπ Gauss's theorem
Total outward flux = Total charge enclosed
∫ D·dS = q_total = 40∏
(given that d = 10 m)