Book about magic with the most used spell "magic whip" [duplicate]

Question

I read a book long time ago, what I remember:

The mages lives in a university, some day they got to tell the people of the town something (I don't remember), and a young girl throws a stone, normally it doesn't hit the mages, but the young girl has magic powers and the stone hit him.

She started to study in the university, receiving bullying from the others, normally fight with some kind of magic whips.

Some other things is that they can share the magic powers, so one can be very powerful if other mages give them the power.

From here the spoilers:

I know that the girl establishes a relationship with the ruler of the university, whom at the first looks like the bad guy, but she discovers that he really is protecting the people, so she helps him, giving them their power.

Answer 1

The Magician's Guild by Trudi Canavan. This is the first book of her Black Magician trilogy.

The girl is Sonea. She is part of a group of children throwing stones, but the stones are all blocked by a magical barrier:

In the corner of her eye she saw an abrupt movement, and turned in time to see Harrin swing his arm forward. A rock flew though the air toward the magicians. Despite knowing what would happen, she held her breath. The stone smacked against something hard and invisible and dropped to the ground. Sonea let out her breath as more of the youths began hurling stones. A few of the robed figures looked up to watch the missiles pattering against the air in front of them. Others regarded the youths briefly, then turned back to their conversations.

when she throws:

Something flipped over in Sonea's belly, and she tightened her grip on the rock. She pulled it free and gauged its weight. A heavy one. Turning to face the magicians, she gathered the anger she felt at being thrown out of her home, all her inbred hate of the magicians, and hurled the stone at the speaker. She traced its path through the air, and as it neared the magicians' barrier, she willed it to pass through and reach its mark. A ripple of blue light flashed outward, then the rock slammed into the magician's temple with a dull thud. He stood motionless, staring at nothing, then his knees buckled and his companion stepped forward to catch him. Sonea stared, her mouth agape, as the older magician lowered his companion to the ground. The jeers of the youths died away. Stillness spread outward like smoke through the crowd.