Question

electric field intensity at any loint due to a short dipole

Answer 1

The below derivation can be used to determine the electric field at any point due to an electric dipole. Thus this is a generalized expression and can be used to determine the electric field due to dipole at equatorial and axial point too.



Consider a short electric dipole AB having dipole moment p. Let the point of interest is at a distance r from the centre O of the dipole. Let the line OP makes an angle θ with the direction of dipole moment p.

Resolve p into two components:

pcosθ along OPpsinθ perpendicular to OP

Point P is on the axial line with respect to pcosθ. So, electric field intensity at P due to short dipole is given by:



Point P is on the equatorial line with respect to psinθ. So, electric field intensity at P due to short dipole is given by:



Since, E1 and E2 are perpendicular to each other, so the resultant electric field intensity is given by:



This is the expression for electric field due to dipole at any point.

Direction of E is given by:



Putting the condition for axial point θ=0 deg, we can obtain the value of electric field due to dipole at axial point. α=0 deg.



Putting the condition for equatorial point θ=90 deg, we can obtain the value of electric field due to dipole at equatorial point. α=90 deg.



Answer 2

Answer: E= KP/r³ (√1+3cos²∅)

Explanation:

Consider a short electric dipole AB having dipole moment P. Let the point of interest be at a distance of r from the centre O of the dipole. Let the line OP make an angle ∅(theta) with the direction of dipole moment P.