An infinitely long wire is kept along `z`-axis from `z= -oo` to `z=+oo`, having uniform linear cahrges density `(10)/(9) nC//m`. The electric field at point `(6 cm,8cm,10 cm)` will be

Options

A. `(120hat(i)+160hat(j)+200hat(k))V//m`
B. `200hat(k)V//m`
C. `(160 hat(i)+120hat(j))V//m`
D. `(120hat(i)+160hat(j))V//m`

Answer

D

Explanation

`E= (lambda)/(2pi epsilon_(0)d)= (2K lambda)/(d)`
`=(2xx9xx10^(9)xx(10//9)xx10^(-9))/(10xx10^(-2))=200 V//m`
As field is radial , out, there is no component of it in `Z` direction.

`vec(E )=(200 cos 53^(@) hat (i)+200 sin 53^(@)hat(j))V//m`
`=(200xx(3)/(5)hat(i)+200xx(4)/(5)hat(j))= (120hat(j)+160hat(j))V//m`