Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $\theta_{(r)}=\frac{Q}{4 \pi \varepsilon_{0} R}\left(a+b(r / R)^{C}\right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ are
A$\left(\frac{1}{2}, \frac{3}{2}, 1\right)$
B$\left(\frac{3}{2},-\frac{1}{2}, 2\right)$
C$\left(\frac{1}{2},-\frac{1}{2}, 1\right)$
D$\left(\frac{1}{2},-\frac{1}{2}, 2\right)$
KVPY 2020, Advanced
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B$\left(\frac{3}{2},-\frac{1}{2}, 2\right)$
b $(b)$ Potential inside a uniformly charged sphere,
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