The potential energy at a point, relative to the reference point is always defined as the negative of work done by the force as the object moves from the reference point to the point considered. The value of potential energy at the reference point itself can be set equal to zero because we are always concerned only with differences of potential energy between two points and the associated change of kinetic energy. A particles A is fixed at origin of a fixed coordinate system. A particle B which is free to move experiences an force `vec(F) = (-(2a)/(r^(3)) + (beta)/(r^(2))) hat(r)` due to particle A where `hat(r)` is the position vector of particle B relative to A. It is given that the force is conservative in nature and _potential energy at infinity is zero. If B has to be removed from the influence of A, energy has to be supplied for such a process. The ionization energy E 0 is work that has to be done by an external agent to move the particle from a distance `r_(0)` to infinity slowly. Here `r_(0)` is the equilibrium position of the particle
If particle B is transferred slowly from point `P_(1) (sqrt2 r_(0), sqrt2 r_(0))` to point `P_(2) ((r_(0))/(sqrt2), (r_(0))/(sqrt2))` in the xy-plane by an external agent, calculate work required to be done by it in the process:

Options

A. `(9 beta^(2))/(64 alpga)`
B. `(beta^(2))/(16 alpha)`
C. `(beta^(2))/(64 alpha)`
D. None of these

Answer

B