hey hermione .........

the following method can be used to get the answer :

see that the fields operating in the system are the two electric fields by the two rings , an external field,and gravity .......

but here for simplicity of the question,the vertical force (net) is zero .... and hence the particle willl move only horizontallly and not vertically ... the initial position being the centre of the ring one and final position being the centre of the ring two ..... so calculate the potentials at the two points and then take the difference and put that equal to the change in kinetic energy ....

1/2 mv² = P_f - P_i

i hope that you get the answer from here ..... if not then we can have more discussion .............

...................keep it cooollll...................