question_answer

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                                   [AIIMS 2005]

A)  

B)                                             

C)  

D)                                             

Correct Answer: A

Solution :

           Inside the shell A, electric field \[{{E}_{in}}=\text{ }0\] 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 \[\left| {{Q}_{A}} \right|<~\left| {{Q}_{B}} \right|\]) 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 \[{{E}_{out}}\]decreases and it becomes zero at x = ¥)