If K e the dielectric constant, then electric field.
E1=14πε0Kq(r2+l2)andE2=14πε0Kq(r2+l2)
E=E1cosθ+E2cosθ
E=14πε0Kq(r2+I2)cosθ+14πε0Kq(r2+l2)cosθ
E=14πε0Kq(r2+l2)×2cosθ
cosθ=OAPA=OA(OP2+OA2)1/2=l(r2+l2)1/2
E=14πε0Kq(r2+l2)×2l(r2+l2)1/2=14πε0K×2ql(r2+l2)3/2
But 2ql=p= electric dipole moment
∴E=14πε0K×p(r2+l2)3/2
E=14πε0Kp(r2)3/2=14πε0Kpr3
Hence, electric field at the equator of dipole is E=14πε0Kpr3