Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 04

Years : DEC 2015

$$F(r) =\log r =\phi \Rightarrow \phi \to f(r) \to x,y,z $$

$\triangledown\phi =\bar i \dfrac {d\phi}{dx}+ \bar j \dfrac {d\phi}{dy} + \bar k\dfrac {d\phi}{dz}=\bar i[ \dfrac 1r \dfrac {dr}{dx}]+\bar j [\dfrac 1r \dfrac {dr}{dy}] + \bar k[\dfrac 1r \dfrac {dr}{dz}] \\ = \bar i \dfrac 1r \dfrac xr + \bar j \dfrac 1r \dfrac yr + \bar k \dfrac 1r\dfrac zr =\dfrac {x\bar i}{r^2}+ \dfrac {y\bar j}{r^2}+\dfrac {z\bar k}{r^2}=\dfrac {\bar r}{r^2}$