An electric charge `2 xx 10^(-8) C` is placed at the point `(1,2,4)`. At the point `(3,2,1)` , the electric
(i) potential will be `50 V`
(ii) field will have no `Y`-component
(iii) field will increase by a factor `K` if the space between the points is filled with a dielectric of constant `K`
(iv) field will be along `Y`-axis

Options

A. field will increase by a factor K if the space between the points is filled with a dielectric of dielectric constant K
B. field will be along the y-axis.
C. potential will be 49.9 V.
D. field will have no y-components.

Answer

C, D

Explanation

c.,d.
`vecr_(p)=hati+2hatj+4hatk,vecr_(q)=3hati+2hatj+hatk`
`[vecr_(q)-vecr_(p)]=sqrt((2)^(2)+(-3)^(2))=sqrt(13)`
As `q=2xx10^(-8)C`,
`V=(1)/(4piepsilon_(0))(q)/([vecr_(q)-vecr_(p)])`
`=(9xx10(9)xx2xx10^(-8))/(sqrt(13))=49.9V`
`vecE=(1)/(4piepsilon_(0))(q)/([vevr_(q)-vecr_(p)]^(2))((vecr_(q)-vecr_(p)))/([vecr_(q)-vecr_(p)])`
`=(1)/(4piepsilon_(0))(q)/([vecr_(q)-vecr_(p)]^(3))(2hati-3hatk)`
(By filling a dielectric of dielectric constant `K`, electric field gets decreases as `E=E_(0)//K` and `Kgt1`)