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Charge density or total charge from a given potential V(r) inside a sphere

This type of question, asked 2 times: 29 Jan 2023, 24 Jan 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    29 Jan 2023

    119
    For a charged spherical ball, electrostatic potential inside the ball varies with rr as V=2ar2+bV = 2ar^{2}+ b. Here, aa and bb are constant and rr is the distance from the center. The volume charge density inside the ball is −λaε- \lambda a\varepsilon. The value of λ\lambda is_____ ε=\varepsilon = permittivity of the medium

  2. Question 2

    24 Jan 2026 S1

    15
    The electrostatic potential in a charged spherical region of radius rr varies as V=ar3+bV = ar^{3}+ b, where aa and bb are constants. The total charge in the sphere of unit radius is α×πa∈0\alpha \times \pi a\in_{0}. The value of α\alpha is ____\_\_\_\_ . (permittivity of vacuum is ∈0\in_{0})

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