A wand is a pen. This wand was a ceremonial wand. The breaking of this wand represents the chamber man no longer signs with the power of the queen. The king will present the chamber man with a new wand and he will cast spells in the kings name..... A pen is a wand. to cast is to shape when wet and let harden as with ink on paper. A word is a spell. And each letter is a rune..... With the wave of a "wand" the chamber man "casts" a "spell".... If you do not think this is magic, watch the changes that can be made by a single signature.
Without the ceremony we would all loose interest in the royals and the magic would cease to work. This is the job of Media.
Big Phama deals in crystal and potion magic. Sorcery, Pharmacia, Pharmacy.
Wands are generally made of holly wood.
The subject of wands in itself is a rabbit hole that's been made quite inaccessible on internet, mainly by Harry Potter. It's easy to find wands for sale, but information about wands is a bit harder to obtain. A pen could be a wand, but it's more than a wand. You can spell words with a pen. Wands can only cast spells.
I don't know the power of spells. Words can be powerful, I know that.