Charges Q, 2Q and 4Q are uniformly distribute | vedclass

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Question

(C) For a uniformly charged solid sphere of radius $a$ and total charge $q$,the electric field at a distance $r$ from the center is given by:$1$. Outs

Vedclass · Accepted Answer

$E_2 > E_1 > E_3$

Vedclass · Answer

(C) For a uniformly charged solid sphere of radius $a$ and total charge $q$,the electric field at a distance $r$ from the center is given by:$1$. Outside $(r \geq a)$: $E = \frac{kq}{r^2}$$2$. Inside $(r For Sphere $1$ $(a = R/2, q = Q)$: Point $P$ is at $r = R$,which is outside $(R > R/2)$.$E_1 = \frac{kQ}{R^2}$For Sphere $2$ $(a = R, q = 2Q)$: Point $P$ is at $r = R$,which is on the surface $(R = R)$.$E_2 = \frac{k(2Q)}{R^2} = \frac{2kQ}{R^2}$For Sphere $3$ $(a = 2R, q = 4Q)$: Point $P$ is at $r = R$,which is inside $(R $E_3 = \frac{k(4Q)R}{(2R)^3} = \frac{4kQR}{8R^3} = \frac{kQ}{2R^2} = \frac{0.5kQ}{R^2}$Comparing the magnitudes: $E_2 = 2\frac{kQ}{R^2}$,$E_1 = 1\frac{kQ}{R^2}$,$E_3 = 0.5\frac{kQ}{R^2}$.Therefore,$E_2 > E_1 > E_3$.

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