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 $- Q_{B}\left( \left| Q_{B} \right| \left| Q_{A} \right| \right).$ The electrical field along a line, (passing through the centre) is

Question

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 $- Q_{B}\left( \left| Q_{B} \right| > \left| Q_{A} \right| \right).$ The electrical field along a line, (passing through the centre) is

Dr. Abubacker · Accepted Answer

(a) Inside the shell $A,$ electric field $E_{in} = 0$
At the surface of shell $A,$
$E_{A} = \frac{kQ_{A}}{r_{A}^{2}} \rightarrow$ [a fixed positive value]
Between the shell $A$ and $B,$ at a distance $x$ from the common centre
$E = \frac{k.Q_{A}}{x^{2}} \rightarrow$ [as $x$ increases $E$ decreases]
At the surface of shell $B,$
$E_{B} = \frac{k.(Q_{A} - Q_{B})}{r_{B}^{2}} \rightarrow$ [a fixed negative value because $\left| Q_{A} \right| < |Q_{B}|$]
Outside the both shell, at a distance $x$ from the common centre
$E_{out} = \frac{k(Q_{A} - Q_{B})}{x^{'2}} \rightarrow$ [As $x'$ increases negative value of $E_{out}$ decreases and it becomes zero at $x = \infty$]

Q. 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 $- Q_{B}\left( \left| Q_{B} \right| > \left| Q_{A} \right| \right).$ The electrical field along a line, (passing through the centre) is

Explanation

Reviewed by Dr. Abubacker

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