The Magicians' Guild: Book 1 of the Black Magician by Trudi Canavan
Each year the magicians of Imardin gather to purge the city streets of beggars, urchins and miscreants. Masters of the disciplines of magic, they know that no one can oppose them. But their protective shield is not as impenetrable as they believe. As the mob is herded from the city, Sonea, a young street girl, furious at the authorities' treatment of her family and friends, hurls a stone at the shield, putting all of her rage behind it. To the amazement of all who watch, there is a flash of blue light and the stone passes straight through the barrier and cracks a magican on the temple, rendering him unconscious. After five hundred years of order, the guild's worst fear has been realised - an untrained magician is loose on the streets. She must be found, and quickly, before her uncontrolled powers unleash forces that will destroy both her, and the city that is her home.