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  4. Consider a uniform spherical volume charge distribution of radius R. Which of the following graphs correctly represents the magnitude of the electric field E at a distance r from the centre of the sphere?

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Q. Consider a uniform spherical volume charge distribution of radius $R.$ Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

KVPYKVPY 2010

Solution:

Electric field due to a volume charge distribution varies with distance $r$ as,
$E = \begin{cases} \frac{kQr}{R^{3}} & \text{ $r<\,R$} \\[2ex] \frac{kQ}{r^{3}} & \text{ $r\le \,R$ } \end{cases}$
or $E \propto\begin{cases}r, & r< R \text { (straight line) } \\ \frac{1}{r^{2}}, & r \geq R \text { (curve) }\end{cases}$