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MHT CET 2024 (2 May, Shift 1) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from MHT CET 2024 (2 May, Shift 1)

Q54MHT CET 2024 · 2 MAY · SHIFT 1Difficult

Electric Potential & Equipotentials

The electrostatic potential inside a charged spherical ball is given by $V = ar^2 + b$ where ' r ' is the distance from its centre and ' $a$ ' and ' $b$ ' are constants. The volume charge density of the ball is [ $\varepsilon_0 =$ permittivity of free space $]$

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Answer: (d)

$E = -\dfrac{dV}{dr} = -2ar$ (radially).
Gauss's law inside a uniform ball: $E = \dfrac{\rho r}{3\varepsilon_0}$ .
$\dfrac{\rho r}{3\varepsilon_0} = -2ar \Rightarrow \rho = -6a\varepsilon_0$
So the answer is (d) $-6a\varepsilon_0$ .

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