The electric field due to a small dipole of length 2l at distance `r ( rgtgtl)` from the centre of the dipole on the axial line is E. What is the distance of the point on the perpendicular bisector of the dipole from its centre in which the electric field intensity is E ?

Explanation

For a small dipole, the electric field intensity at a disatance r from the centre of the dipole on the axial line,
`E=(2p)/(4pi in _(0)r^(3))`
Let the electric field intensity at distance r' from the centre the dipole on the perpendicular bisector of the dipole be `E'` .
`therefore E' =(p)/(4pi in_(0) (r')^(3))[because E=E']`
or , `r'=(r)/( root(3)(2))`
Hence, required distance `=(r )/(root(3)(2))`.