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A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x \lt R$, the electric field is directly proportional to
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$x$
Let sphere has uniform chare density $\rho\left(=\frac{3 Q}{4 \pi R^3}\right)$ and $E$ is the electric field at distance $x$ from the centre of the sphere.
Applying Gauss law
$E .4 \pi x^2=\frac{q}{\varepsilon_0}=\frac{\rho V^{\prime}}{\varepsilon_0}=\frac{\rho}{\varepsilon_0} \times \frac{4}{3} \pi x^3$
$\left(V^{\prime}=\right.$ Volume of dotted sphere $) \therefore \quad E=\frac{\rho}{3 \varepsilon_0} x \Rightarrow$\(\mathrm{E} \propto \mathrm{X}\)
Applying Gauss law
$E .4 \pi x^2=\frac{q}{\varepsilon_0}=\frac{\rho V^{\prime}}{\varepsilon_0}=\frac{\rho}{\varepsilon_0} \times \frac{4}{3} \pi x^3$
$\left(V^{\prime}=\right.$ Volume of dotted sphere $) \therefore \quad E=\frac{\rho}{3 \varepsilon_0} x \Rightarrow$\(\mathrm{E} \propto \mathrm{X}\)
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