First slide

Electric field

Question

Two concentric conducting thin spherical shells A, and B having radii $r_{A} and r_{B} (r_{B} > r_{A})$ are charged to $Q_{A} a n d - Q_{B} (|Q_{B}| > |Q_{A}|)$ The electrical field along a line, (passing through the centre) is

Difficult

A
B
C
D

Solution

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 shells A and B, at a distance x from the common centre
$E = \frac{k \cdot Q_{A}}{x^{2}} ⟶ (as x increases E decreases)$
At the surface of shell B,
$E_{B} = \frac{k \cdot (Q_{A} - Q_{B})}{r_{B}^{2}} ⟶$ $(a fixed negative value because |Q_{A}| < |Q_{B}|) .$
Outside the both shells, at a distance x from the common center
$E_{out} = \frac{k (Q_{A} - Q_{B})}{x^{, 2}} ⟶ (a s x' i n c r e a s e s n e g a t i v e v a l u e o f E_{o u t} d e c r e a s e s a n d i t b e c o m e s z e r o a t x' \to \infty)$

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