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  • charge q is uniformly distributed within an insulating sphere of radius r . apply gauss's theorem to find electric feild,due to this charge distrubution,at a point distance 'r' from the

Charge q is uniformly distributed within an insulating sphere of radius r. Apply Gauss's theorem to find the electric field, due to this charge distribution, at a point distance 'r' from the center of the sphere, where (a) r> R, (b) r=R,(c)0<r<R.

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Given- 

  • Total charge =  q
  • Radius of the sphere =  R
  • The charge is uniformly distributed inside the sphere

Solution- According to Gauss law, $\oint \vec{E} \cdot d\vec{A} = \dfrac{q_{\text{enc}}}{\varepsilon_0}$

a) $E = \dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{q}{r^2}$

b) $E = \dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{q}{R^2}$

c) Charge density: $\rho = \dfrac{q}{\frac{4}{3}\pi R^3}$
Enclosed charge: $q_{\text{enc}} = \rho \cdot \frac{4}{3}\pi r^3 = q \cdot \frac{r^3}{R^3}$
Using Gauss’s law: $E \cdot 4\pi r^2 = \frac{q r^3}{\varepsilon_0 R^3}$

Posted by

Saniya Khatri

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