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

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Detailed Solution

Inside the shell A, electric field $E in = 0$

At the surface of shell A,
$E A = k Q A r A 2 →$ (a fixed positive value)
Between the shell A and B, at a distance x from the common centre
$E = k ⋅ Q A x 2 →$ (asx increases E decreases)
At the surface of shell B,
$E B = k ⋅ Q A − Q B r D 2 →$ (a fixed negative value because $Q A < Q B$
Outside the both shell, at a distance x from the common centre
$E out = k Q A − Q B x ′ 2 →$ (asx' increases negative value of $E out$ decreases and it becomes zero at $x = ∞)$