Assuming the formula are right, I do the following to make the program (as you wrote it) to work. Starting at the "For loop".
For[i = 1, i < step + 1, i++,
(*Assigned integration to variable ans to make the next assignemnt \
easier to understand.*)
ans = FindRoot[
1/2 Integrate[ell^2, {phi, start, x}] == a*b*Pi/step, {x, 0.1}];
(*We had solved for x in the previous line, so we need to extract \
the number other wise we would have {x->number}, which can't be \
re-used.*)
start = x /. ans[[1]];
(*This is just a debug print. You could assign the answers into a \
list.*)
Print[i, " ", start]]
Are these the answers your anticipated (i,start) pairs? You can remove the 0.I with the Chop command.
(1, 0.401966)
(2, 0.727518+0. I)
(3, 0.96804+0. I)
(4,1.14777+0. I)
(5, 1.28976+0. I)
(6,1.40974+0. I)
(7, 1.51829+0. I)