Question

At a far away distance r along the axis from a electric dipole electric field is E. Find the electric field at distance 2r along the perpendicular bisector.

Answer 1

Electric field at distance 2r along the perpendicular bisector:

Along the axis dipole, $E = -\frac{2kp}{r^3}$ --- Equation 1

Along the perpendicular bisector, Electric field at distance 2r=$E'=\frac{kp}{(2r)^3} = \frac{2kp}{16r^3} =-\frac{E}{16}$ (Putting Equation 1)

Answer 2

The electric field at distance 2r along the perpendicular bisector is E' = -E / -16`

Explanation:

Along the axis of dipole,

E = 1 / 4πε0 2p / r^3   -------- (1)

This electric field is in the direction of p along the perpendicular bisector at a distance 2r.

E' = 1 / 4πε0 − p(2r)^3     --------(2)

From equation i and ii we can see that

E' = E / 16

More over E'is∈ the opposite direction of p.

E' = -E / -16`

Hence the electric field at distance 2r along the perpendicular bisector is E' = -E / -16`