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Two concentric conducting thin spherical shells $A$ and $B$ having radii ${r_A}$ and ${r_B}$ (${r_B} > {r_A})$ are charged to ${Q_A}$ and $ - {Q_B}$$(|{Q_B}|\, > \,|{Q_A}|)$. The electrical field along a line, (passing through the centre) is
Solution
(a) Inside the shell $A$, electric field $E_{in} = 0$
At the surface of shell $A$,
${E_A} = \frac{{k\,{Q_A}}}{{r_A^2}}$ $\xrightarrow{\,}$ (a fixed positive value)
Between the shell $A$ and $B$, at a distance $x$ from the common centre
$E = \frac{{k.\,{Q_A}}}{{{x^2}}}$ $\xrightarrow{\,}$ (as $x$ increases $E$ decreases)
At the surface of shell $B$,
${E_B} = \frac{{k.\,({Q_A} – {Q_B})}}{{r_B^2}}$ $\xrightarrow{\,}$ (a fixed negative value because $|QA| < |QB|$)
Outside the both shell, at a distance $x$ from the common centre
${E_{out}} = \frac{{k({Q_A} – {Q_B})}}{{x{'^2}}}$ $\xrightarrow{\,}$ (as $x$ increases negative value of Eout decreases and it becomes zero at $x = \infty$)
