three dipoles each of dipole moment of magnitude p are placed tangentially on a circle of radius r in its plane positioned at equal angle from each other then the magnitude of electric field intensity at the centre of the circle will be

The electric field intensity at the center of the circle due to a dipole is given by the formula:

E = kp/r^3

where: k is Coulomb's constant, p is the dipole moment, and r is the distance from the dipole (which is the radius of the circle in this case).

Since there are three dipoles, and they are positioned symmetrically around the circle, the electric field intensity at the center due to each of them will be in a direction perpendicular to the line joining the dipole and the center.

Because of this symmetry, the horizontal components of the electric field intensity due to each dipole will cancel out, while the vertical components will add up.

Since the dipoles are positioned at equal angles from each other, the angle between the direction of the electric field intensity due to each dipole and the vertical direction is 30 degrees.

Therefore, the total electric field intensity at the center of the circle is:

E_total = 3Ecos(30) = 3(kp/r^3)cos(30) = 3(kp/r^3)(√3/2) = √3kp/r^3

So, the magnitude of the electric field intensity at the center of the circle is √3kp/r^3.