question_answer

A sphere \[{{\mathbf{S}}_{\mathbf{1}}}\] of radius\[{{\mathbf{r}}_{\mathbf{1}}}\] encloses a charge Q. If there is another concentric sphere of radius\[{{\mathbf{r}}_{\mathbf{2}}}\mathbf{(}{{\mathbf{r}}_{\mathbf{2}}}\mathbf{>}{{\mathbf{r}}_{\mathbf{1}}}\mathbf{)}\] there be no additional charges between \[{{\mathbf{S}}_{\mathbf{1}}}\] and \[{{\mathbf{S}}_{\mathbf{2}}}\] find the ratio of the electric flux through \[{{\mathbf{S}}_{\mathbf{1}}}\] and \[{{\mathbf{S}}_{\mathbf{2}}}\]

Answer:

                From Gauss's theorem, Electric flux through\[{{S}_{1}},\]\[{{\phi }_{1}}=\frac{{{q}_{1}}}{{{\varepsilon }_{0}}}=\frac{Q}{{{\varepsilon }_{0}}}\] Electric flux through \[{{S}_{2}}\],\[{{\phi }_{2}}=\frac{{{q}_{2}}}{{{\varepsilon }_{0}}}=\frac{Q}{{{\varepsilon }_{0}}}\] \[\therefore \]Ratio, \[\frac{{{\phi }_{1}}}{{{\phi }_{2}}}=\frac{Q/{{\varepsilon }_{0}}}{Q/{{\varepsilon }_{0}}}=1:1\]