Electric field of an electric dipole for axial points
Two charges 10μC are placed 5.0mm apart.Determine the electric field at a point P on the axis of the dipole 15cm away from its centre O on the side of the positive charge. Solution: Field at P due to charge +10μC: =4π(8.854×10−12C2N−1m−2)10−5×(15−0.25)2×10−4m21 =4.13×106NC−1along BP Field at P due to charge −10μC =4π(8.854×10−12C2N−1m−2)10−5×(15+0.25)2×10−4m21 =3.86×106NC−1 along PA The resultant electric field at P due to the two charges at A and B is =2.7×105NC−1 along BP. In this example, the ratio OP/OB is quite large (= 60). Thus, we can expect to get approximately the same result as above by directly using the formula for electric field at a far-away point on the axis of a dipole.For a dipole consisting of charges q,2a distance apart, the electric field at a distance r from the centre on the axis of the dipole has a magnitude E=4πϵ0r32p(r/a>>1) where p=2aq is the magnitude of the dipole moment.The direction of electric field on the dipole axis is always along the direction of the dipole moment vector (i.e., from −qtoq). Here, p=10−5C×5×10−3m=5×10−8Cm E=2.6×105NC−1 Along the dipole moment direction AB, which is close to the result obtained earlier.
Electric field of an electric dipole for equatorial points
Two charges each of 10 C are placed 5.0 mm apart.Determine the electric field at a point Q, 15 cm away from O on a line passing through O and normal to the axis of the dipole, E=4πϵ0r3p(r/a>>1) =4π×(8.854×10−12C2N−1m−2)5×10−8×(15)3×10−6m31 =1.33×105NC−1 The direction of electric field in this case is opposite to the direction of the dipole moment vector.
Electric field due to a dipole
E=4πϵ01r3p3cos2θ+1 where θ is the angle between the distance vector and dipole.
Potential due to a dipole at a general point
Potential due to a dipole is given by: V≈4πεor2pcosθ where p: electric dipole moment θ: angle made by the line joining center of dipole and the point with the dipole moment vector r: distance between the center of dipole and the point Note: Approximation is made that the length of dipole is negligible as compared to the distance of the point from the dipole.