The magnitude of the electric field at a distance r on the equatorial line of a short electric dipole is E . A point charge Q is brought from infinity to a point on the axial line of the same dipole at a distance r 3 from its center. If the work done by the external agent is W = Q E r , the value of is

Step-by-step solution

The magnitude of the electric field on the equatorial line of a short dipole at a distance r is: E = kp r^3 From this, we can write kp = E r^3 . The electrostatic potential on the axial line of the short dipole at a distance x = r 3 from the center is: V = kp x^2 = kp ( r 3 )^2 = 9kp r^2 The work done by an external agent in bringing a point charge Q from infinity to this point is: W = Q V = Q(V - V_ ) = Q ( 9kp r^2 - 0 ) = 9Qkp r^2 Substituting kp = E r^3 into the work equation: W = 9Q(E r^3) r^2 = 9 Q E r Compari