Electric potential & energy

A point charge q_1 is held stationary at the origin. A second charge q_2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 xx 10^-8 J . When the second charge is moved to point b, the electric force on the charge does 4.2 xx 10^-8 J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?

Is it possible to have an arrangement of two point charges separated by finite distances such that the electric potential energy of the arrangement is the same as if the two charges were infinitely far apart? What if there are three charges?

Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them so that the electrical potential energy of the system is a minimum

If V and u are electric potential and energy density, respectively, at a distance r from a positive point charge, then which of the following graph is correct ?

A uniform electric field E_0 is directed along positive y-driection. Find the change in electric potential energy of a positive test charge q_0 when it is displaced in this field from y_i=a to y_f=2a along the y-axis.

A uniform electric field E_0 is directed along positive y-driection. Find the change in electric potential energy of a positive test charge q_0 when it is displaced in this field from y_i=a to y_f=2a along the y-axis.

Assertion: Two charges -q each are fixed points A and B. When a third chrge -q is moves from A to B, electrical potential energy first decreases than increases, Reason: Along the line joining A and B, third charge is stable equilibrium position at centre.

Four charges are placed at four corners of a square as shown in figure. The side of the square is a. Two charges are positive and two are negative, but their magnitudes are the same. Now, an external agent starts decreasing all the sides of the square slowly and at the same rate. What happens to the electrical potential energy of the system and what will be the nature of work done by the agent?

Two neutral particles are kept 1m apart. Suppose by some mechanism some charge is transferred from one particle to the other and the electric potential energy lost is completely converted into a photon. Calculate the longest and the next smaller wavelength of the photon possible. h=6.63xx10^(-34)Js .