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In the figure, the inner (shaded) region A represents a sphere of radius r A = 1, within which the electrostatic charge density varies with the radial distance r from the center as ρ A = kr, where k is positive. In the spherical shell B of outer radius r B , the electrostatic charge density varies as ρ B = r k 2 . Assume that dimensions are taken care of . All physical quantities are in their SI units. Which of the following statement(s) is (are) correct ?

1. If r B = 2 3 , then the electric field is zero everywhere outside B.
2. If r B = 2 3 , then the electric potential just outside B is 0 k ∈ .
3. If r B = 2. then the total charge of the configuration is 15 π k.
4. If r B = 2 5 , then the magnitude of the electric field just outside B is 0 k 13 ∈ π

Correct answer: If r B = 2 3 , then the electric potential just outside B is 0 k ∈ .

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