What do you mean by "white magic" though? I understand that this is all you are interested in, but what you mean by "white magic" and what I mean by "white magic" may be two very different things. Please describe what you mean.
Also, the "water, earth, fire, air" series of elements are generally called the "Classical elements." Several cultures used those elements, but most of magick more specifically takes them from classical Greek thought. Those aren't the only elements, though. In China the elements are Wood, Fire, Earth, Metal, and Water. The Babylonians thought of the sky and the wind as being different elements, rendering their list as Sea, Earth, Fire, Sky, and Wind. In the West the 5th element of spirit or aether is sometimes included, but in Japan it is viewed as a necessary element, and their elemental listing goes as Earth, Water, Fire, Wind, and Void. In Hinduism the elements are conceived of as being Earth, Water, Fire, Air, Sound/Spirit, Lightness, and Thought/Space. This in turn influenced the elements of Theravada Buddhism in which they are called the Kalapas of Earth, Water, Fire, Air, Color, Smell, Taste, and Nutritive Essence (stuff that keeps you alive).
There's a lot of different ways of conceiving of magick and energies and elements and everything else, so you should try to be as specific as possible.