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Standard XII

Physics

Electric Field Due to Charge Distributions - Approach

The magnitude...

Question

The magnitude of the electric field inside ( $r < R$ ) the sphere is $E = \frac{A R^{3}}{X ε_{0}}$ . Find $X$ ?

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Solution

For $r < R$ ,
$q_{i n} = \int ρ d V = \int_{0}^{r} A r^{2} (4 π r^{2}) d r = \frac{4 π A r^{5}}{5}$
$∴ E = \frac{q_{i n}}{ϵ 4 π r^{2}} = \frac{A r^{3}}{5 ϵ}$

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Similar questions

Q. The magnitude of electric field as a function of the distance r inside the sphere is given by :

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The magnitude of the electric field inside (r<R) the sphere is E=AR3Xε0. Find X?

For r<R,qin=∫ρdV=∫r0Ar2(4πr2)dr=4πAr55∴E=qinϵ4πr2=Ar35ϵ

The magnitude of the electric field inside ( $r < R$ ) the sphere is $E = \frac{A R^{3}}{X ε_{0}}$ . Find $X$ ?

For $r < R$ ,
$q_{i n} = \int ρ d V = \int_{0}^{r} A r^{2} (4 π r^{2}) d r = \frac{4 π A r^{5}}{5}$
$∴ E = \frac{q_{i n}}{ϵ 4 π r^{2}} = \frac{A r^{3}}{5 ϵ}$