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A solid sphere of radius $r_1=1 \mathrm{~cm}$ carries charge distributed uniformly over it with density $\rho_1=-3 \mathrm{C} / \mathrm{cm}^3$. It is surrounded by a concentric spherical shell of radius $r_2=2 \mathrm{~cm}$ carrying uniform charge density $\rho_2=\frac{1}{2} \mathrm{C} / \mathrm{cm}^2$. If $E_d$ denotes the magnitude of the electric field at distance $d$ from the common centre of the spheres, then
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Verified Answer
The correct answer is:
$E_d=\frac{d}{\varepsilon_0}, d \leq 1 \mathrm{~cm}$
Electric field at a point inside inner sphere is only due to charge enclosed.
We use Gauss' law to get,
$$
E=\left(\frac{q}{4 \pi \varepsilon_0 R^3}\right) r=\frac{\rho_R}{3 \varepsilon_0}
$$
Here,
$$
\rho=-3\left(\frac{\mathrm{C}}{\mathrm{cm}^3}\right)
$$
So,
$$
E=\frac{-d}{\varepsilon_0} \text { or }|\mathbf{E}|=\frac{d}{\varepsilon_0}
$$
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