Show that, for a given dipole, V & E cannot have the same magnitude at distance less than 2m from the dipole. Suppose that the distance is `sqrt(5)m`, determine the directions along which V & E are equal in magnitude.

Answer

`45^(@), 135^(@), 225^(@), 315^(@)`

Explanation

`|V_(P)|=|E_(P)|`
`(KP cos theta)/r^(2)=(KP)/r^(3)sqrt(1+3cos^(2) theta), cos theta=(1)/sqrt(r^(2)-3)`
`r^(2)-3 ge 1, r ge 2`
Now `cos theta=1/sqrt(r^(2)-3)(r=sqrt(5))=1/sqrt(2)`
then `theta=45^(@), 135^(@), 225^(@), 315^(@)`