A sphere of radius R has a uniform distribution of electric charge in its volume. At a distance x fr

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1. Electric Charges and Fields

medium

A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to

$\frac{1}{{{x^2}}}$

$\frac{1}{x}$

$x$

${x^2}$

(AIIMS-1997)

Solution

(c) Let sphere has uniform chare density $\rho \,\left( { = \frac{{3Q}}{{4\pi {R^3}}}} \right)$ and $E$ is the electric field at distance $x$ from the centre of the sphere.
Applying Gauss law
$E.\,4\pi \,{x^2} = \frac{q}{{{\varepsilon _0}}} = \frac{{\rho V'}}{{{\varepsilon _0}}} = \frac{\rho }{{{\varepsilon _0}}} \times \frac{4}{3}\pi {x^3}$
($V' = $ Volume of dotted sphere)
$E = \frac{\rho }{{3{\varepsilon _0}}}x$ $==>$ $E \propto \,x$

Standard 12

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(AIIMS-2005)

A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to

Solution

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