As charge `q=1muC` is placed at point `(1m,2m,4m)`. Find the electric field at point `P(0,-4m,3m)`

Explanation

Here `vecr_(q)=hati+2hatj+4hatk`
and `vecr_(p)=-4hatj+3hatk`
`:.vecr_(p)-vecr_(q)=-hati-6hatj-hatk`
or
`|vecr_(p)-vecr_(q)|=sqrt((-1)^(2)+(-6)^(2)+(-1)^(2))=sqrt(38)m`
Now `vecE=1/(4 pi epsilon_(0)) q/(|vecr_(p)-vecr_(q)|^(3))(vecr_(p)-vecr_(q))`
Substituting the values, we have
`vecE=((9xx10^(9))(1.0xx10^(-6)))/((38)^(3//2)=(-hati-6hatj-hatk)`
`vecE=(-38.42hati-231.52hatj-38.42hatk)N/C`