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 $-Q_B(|Q_B|>|Q_A|)$. The electrical field along a line, (passing through the centre) is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Inside the shell A, electric field $E_{in}=0$

At the surface of shell A,
$E_A=\frac{k{Q}_A}{r_A^2}⟶$ (a fixed positive value)
Between the shell A and B, at a distance x from the common centre
$E=\frac{k{Q}_A}{x^2}⟶$ (as x increases E decreases)
At the surface of shell B,
$E=\frac{k.(Q_A-Q_B)}{r_B^2}⟶$ (a fixed negative value because $|Q_A|<|Q_B|$)
Outside the both shell, at a distance x from the common centre
$E=\frac{k(Q_A-Q_B)}{x^{{}^{\prime 2}}}⟶$ (as $x^{{}^{\prime }}$ increases negative value of $E_{out}$ decreases and it becomes zero at $x=\infty$)