The incident of Laxmana drawing a line around Sita (Laxmana Rekha) is very popular. However, it is not part of the original Ramayana. Valmiki never mentioned any such thing. Here I am quoting from Valmiki Ramayana.
Sita said very harsh words to Laxmana as he initially refused to go in search of Rama. Then Laxmana said -
Valmiki Ramayana, Aranyakandam, Chapter 45 (end part)
I shall go where Kākuthstha is, may good betide thee, O thou the best of damsels! May the deities of the forest protect thee, O thou of expansive eyes! Many a bad omen appear before me. May I see thee again when I shall come back with Rāma." Being thus accosted by Lakshmana the daughter of Janaka replied weeping and being bathed in tears. "Without Rāma, O Lakshmana, I shall drink virulent poison, enter fire or dive into the Godaveri. I shall destroy this body either by hanging or by falling down from the top of a high object. I shall never be able to touch another man but Rāma." Speaking thus unto Lakshmana, Sitā, being enveloped with grief, weeping, struck her belly* with her hands. Seeing the daughter of Janaka of expansive eyes weep thus in pitiable accents, Lakshmana losing his attention began to console her. Afterwards the pure-hearted Lakshmana, having control over his senses, saluting Sitā with clasped palms and bending low a little proceeded where Rāma was, casting again and again his glance upon her as he went. - Valmiki Ramayana III.XLV
*(Properly it should be "struck her breast." But it has a special significance here, i.e.—she would not be satisfied until her belly be filled with all the Rākshasas slain.—Translator's note.)
This is the end of the chapter 45. So, as you see there is no Laxman Rekha, there can't be any magical power behind it. These are all later additions.
Reference -