question_answer 21)

Two charges – q and + q are located at points (0, 0, –a) and (0, 0, a), respectively. (a) What is the electrostatic potential at the points (0, 0, z) and (x, y, 0)? (b) Obtain the dependence of potential on the distance r of a point from the origin when r1a >> 1. (c) How much work is done in moving a small test charge from the point (5, 0, 0) to (–7, 0, 0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?  

Answer:

(a) Point (0, 0, z) lies on the axis of the given dipole.                 Potential on a point on the axial line of dipole,                                 where p = q × 2a                 Point (x, y, 0) means normal to the dipole, so the potential is zero.                 (b) Consider P to be the point of observation at a distance r from the centre (O) of the electric dipole. Let OP make an angle  with the dipole moment  and r1, r2 be the distances of point P from ? q charge and + q charge respectively.                 Potential at P due to ?q charge,                                                 Potential at P due to + q charge,                                 Potential at P due to the dipole.                                 V = V1 + V2                 Or                 Or                 Now draw a perpendicular from A which meets the line OP at C when produced backward. Also draw                 Then, r1=                                 (from )                 and r2 = BP = DP = OP ? OD                                 (from )                                                                                                 (dipole moment, )                 If r > > 1, then                 When  the dependence of the potential on distance is of type.                 (c) Zero                 Answer does not change because in electrostatics, the work done does not depend upon actual path, it simply depends upon the initial and final positions.