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(B) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dr}$.Given $V = 2ar^2 + b$,differentiating with respect to

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$12$

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(B) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dr}$.Given $V = 2ar^2 + b$,differentiating with respect to $r$ gives $E = -\frac{d}{dr}(2ar^2 + b) = -4ar$.According to Gauss's Law for a uniformly charged sphere,the electric field inside is given by $E = \frac{\rho r}{3\varepsilon}$,where $\rho$ is the volume charge density.Comparing the two expressions for $E$: $-4ar = \frac{\rho r}{3\varepsilon}$.Solving for $\rho$: $\rho = -12a\varepsilon$.Comparing this with the given form $\rho = -\lambda a\varepsilon$,we find $\lambda = 12$.

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