The Magicians' Guild by Trudi Canavan (Black Magician #1)

Each year the magicians of Imardin gather to purge the city streets of vagrants, 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, a young street girl, furious at the authorities' treatment of her family and friends, hurls a stone at the shield, putting all her rage behind it. To the amazement of all who bear witness, the stone passes unhindered through the barrier and renders a magician unconscious. 

It is an inconceivable act, and 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.

A book by author Trudi Caravan.