A dipole is placed in the field of a point charge, the distance between the dipole and the field source being much greater than the dipole separation. Find the force acting on the dipole and the torque, if the dipole is arranged:
In the direction of the line of force.

Explanation

It is evident from Fig. 24.8b that in this case two forces act on the dipole in the direction of the radius vector. Hence it is clear that in the latter case the torque is zero, and the resultant acts in the direction of the radius to the source. The resultant can be found by two methods.
One may use the Coulomb law:
`F=F_(-)+F_(+)=-(Qq)/(4pi epsi_(0)(r-l//2)^(2))+(Qq)/(4pi epsi_(0)(r+l//2)^(2))`
`=-(2Qrql)/(4pi epsi_(0)(r^(2)-l^(2)//4)^(2))`

Noting that the problem stipulates that `l lt lt r`, we obtain
`F=0(2Qrql)/(4pi epsi_(0)r^(4))=-(2Q p_(0))/(4pi epsi_(0)r^(3))`
The same result may be obtained from formula (37.15), if the derivative is substituted for the ratio of increments. We have
`F=p_(e)=(dE)/(dr)=Pe(d)/(dr)((Q)/(4pi epsi_(0)r^(2)))=-(2Qp_(e))/(4pi epsi_(0)r^(3))`