tolkiens legendarium - How did the Witch King break Gandalf's staff in the movie?

In the movie, the Witch King breaks Gandalf's staff. How did this happen and why (since it's not in the book)?

Answer

While Gandalf faces the Witch King in Minas Tirith, there is no record of Gandalf's staff being broken. The flaming sword is seen in the scene in the book, from Return of the King, The Siege of Gondor:

'You cannot enter here,' said Gandalf, and the huge shadow halted. 'Go back to the abyss prepared for you! Go back! Fall into the nothingness that awaits you and your Master. Go!' The Black Rider flung back his hood, and behold! he had a kingly crown; and yet upon no head visible was it set. The red fires shone between it and the mantled shoulders vast and dark. From a mouth unseen there came a deadly laughter. 'Old fool!' he said. 'Old fool! This is my hour. Do you not know Death when you see it? Die now and curse in vain!' And with that he lifted high his sword and flames ran down the blade. Gandalf did not move. And in that very moment, away behind in some courtyard of the City, a cock crowed. Shrill and clear he crowed, recking nothing of wizardry or war, welcoming only the morning that in the sky far above the shadows of death was coming with the dawn.

After that scene, Rohan arrives, and the Witch King flies off to handle them.

The Witch King's ability to destroy others' weapons is found in the books, however. From The Fellowship of the Ring, Flight to the Ford:

Then the leader, who was now half across the Ford, stood up menacing in his stirrups, and raised up his hand. Frodo was stricken dumb. He felt his tongue cleave to his mouth, and his heart labouring. His sword broke and fell out of his shaking hand. The elf-horse reared and snorted. The foremost of the black horses had almost set foot upon the shore.

From the same chapter, after the wraiths are driven off, Aragorn is examining the cloak left by the Witch King:

Look!" he cried; and stooping he lifted from the ground a black cloak that had lain there hidden by the darkness. A foot above the lower hem there was a slash. "This was the stroke of Frodo's sword," he said. "The only hurt that it did to his enemy, I fear; for it is unharmed, but all blades perish that pierce that dreadful King.

It's likely that Jackson interpreted Gandalf's raised staff as a "blade to pierce" the Witch King. It doesn't say in the books whether the WK could destroy an Istar's staff, but I think that scene is Jackson's interpretation of these scenes in the book.