question_answer

The electric field at a distance r from the centre in the space between two concentric metallic spherical shells of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] carrying charge \[{{Q}_{1}}\] and \[{{Q}_{2}}\]is \[({{r}_{1}}<r<{{r}_{2}})\]

A) \[\frac{{{Q}_{1}}+{{Q}_{2}}}{4\pi {{\in }_{0}}{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

B)        \[\frac{{{Q}_{1}}+{{Q}_{2}}}{4\pi {{\in }_{0}}{{r}^{2}}}\]

C) \[\frac{{{Q}_{1}}}{4\pi {{\in }_{0}}{{r}^{2}}}\]        

D)        \[\frac{{{Q}_{2}}}{4\pi {{\in }_{0}}{{r}^{2}}}\]

Correct Answer: C

Solution :

[c] \[\int{E.dx=\frac{{{Q}_{1}}}{{{\in }_{0}}}}\]\[\Rightarrow \]\[E=\frac{{{Q}_{1}}}{4\pi {{r}^{2}}{{\in }_{0}}}\]