A) \[K\,\log \frac{r}{{{r}_{0}}}+{{V}_{0}}\]
B) \[K\,\log \frac{{{r}_{0}}}{r}+{{V}_{0}}\]
C) \[K\,\log \frac{r}{{{r}_{0}}}-{{V}_{0}}\]
D) \[\log \frac{{{r}_{0}}}{r}-{{V}_{0}}r\]
Correct Answer: A
Solution :
[a] We know that intensity is negative gradient of potential, i.e., \[I=-(dV/dr)\]and as here\[I=-(K/r)\], so \[\frac{dV}{dr}=\frac{K}{r},i.e.,\int{dV=Ki}\int{\frac{dr}{r}}\] or \[V-{{V}_{0}}=K\log \frac{r}{{{r}_{0}}}\] so \[V=K\log \frac{r}{{{r}_{0}}}+{{V}_{0}}\]
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