I've seen two ways to express this recently, and out of curiosity, I wondered which was the ''correct'' way to present it. \(\frac{\epsilon_0}{2}E^2=u_e\) Which wiki is familiar with. I saw another way of writing it, \(\frac{1}{2}\epsilon_0E^2=u_e\) Which is slightly different. Which way is the correct way or writing it?
Do you think there's an important difference between the following notations, Green Destiny? \(\frac{1}{2}x,\qquad \frac{x}{2},\qquad x/2\) Which would you prefer?
I think you're asking me if they have a mathematical difference - the answer is obviously no. I was simply wondering if there was a preferred notation. I think by preferred, I mean the original derivation. I just want to memorize it the way it was intended.
What do you think is more important, Green Destiny: the mathematical content of the formula, or the way it is written?
Why do you think it is important to remember how the formula in your opening post was written when it was first derived? Do you think most physicists would do that?
When I was younger, our lecturer always made a huge deal out of memorizing our equations. If I was able to cut down something and memorize it, to me that would make things simpler if there was one way I could universally represent it and not be worried.
Would you worry if something was written as \(\frac{x}{2}\) rather than \(\frac{1}{2}x\)? What, in particular, would you be worried about?
You've probably worked out by now my answer to your initial question "Which is the 'correct' way to present the equation?" Answer: both are equally correct. They have exactly the same mathematical content, so it doesn't matter which way you write it. Your question is equivalent to asking which of the following sentences is "correct": "I am going to the beach with my brother." "My brother and I are going to the beach together."
I'm probably nitpicking, but the expressions in the OP aren't the E field strength, but the energy density of the E field.
