GATE 2015 EE -SET 1 – Question 4

Solution : ∇ .$$\overline{F}$$ = $$\frac{1}{^{r}2}$$ $$ \frac{$$\partial }{$$\partial r} $$( r2 x  $$\bar{F_{r}}$$)

=$$\frac{1}{^{r}2}$$ $$ \frac{$$\partial }{$$\partial r} $$( r2 x $$\frac{1}{r^{2}}$$ $$\bar{r}$$

∇ .$$\overline{F}$$ = $$\frac{1}{^{r}2}$$ $$ \frac{$$\partial }{$$\partial r} (1) = 0.

Using Gauss theorem