A) Both the spheres will have the same charge of \[10\,C\]
B) Surface charge density on the \[20\,cm\] sphere will be greater than that on the \[15\,cm\] sphere
C) Surface charge density on the \[15\,cm\] sphere will be greater than that on the \[20\,cm\] sphere
D) Surface charge density on the two spheres will be equal
Correct Answer: C
Solution :
After redistribution, charges on them will be different, but they will acquire common potential i.e. \[k\frac{{{Q}_{1}}}{{{r}_{1}}}=k\frac{{{Q}_{2}}}{{{r}_{2}}}\] Þ \[\frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\] As \[\sigma =\frac{Q}{4\pi \,{{r}^{2}}}\] Þ \[\frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{{{Q}_{1}}}{{{Q}_{2}}}\times \frac{r_{2}^{2}}{r_{1}^{2}}\] Þ \[\frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{{{r}_{2}}}{{{r}_{1}}}\] Þ \[\sigma \propto \frac{1}{r}\] i.e. surface charge density on smaller sphere will be more.
You need to login to perform this action.
You will be redirected in
3 sec
