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Q.

A solid non conducting sphere of radius R has a spherical cavity of radius $\frac{R}{2}$ as shown in figure and the remaining material has uniform charge distribution of charge density $ρ$ . The energy density of electric field inside the cavity is

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a

$\frac{ρ^{2} R^{2}}{18 ε_{0}}$

b

$\frac{ρ^{2} R^{2}}{72 ε_{0}}$

c

Zero

d

$\frac{ρ^{2} R^{2}}{36 ε_{0}}$

answer is C.

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Detailed Solution

Intensity of electric field inside the cavity is uniform and $E = \frac{ρ (R / 2)}{3 ε_{0}} = \frac{ρ}{6 ε_{0}}$
Energy density of electric field $U = \frac{1}{2} ε_{0} E^{2} = \frac{1}{2} ε_{0} \frac{ρ^{2} R^{2}}{36 ε_{0}^{2}} = \frac{ρ^{2} R^{2}}{72 ε_{0}}$

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A solid non conducting sphere of radius R has a spherical cavity of radius R2 as shown in figure and the remaining material has uniform charge distribution of charge density ρ. The energy density of electric field inside the cavity is