Why does moving a bar magnet through a larger loop of wire generate more current than through a smaller wire at the same speed? Why does moving a bar magnet through a larger loop of wire generate more current than through a smaller wire at the same speed? 
A theoretical, rather than rigorously mathematical explanation would be great!
 A: Imagine a small loop right above a magnet. When the loop is small the flux is small lets say its value is "F" (unit in tesla m²). When it gets closer to the magnet its value doubles, so it becomes "2F". Lets say that happened in 1 s, so the force per charge produced on the loop is on average (2F-F)/1s = 1 V. 
Now lets get larger loop and do the same thing. Lets suppose we picked a loop that will have two times the flux of the small loop at the same distance, so its flux its 2F, now lets get closer to the magnet as we did with the smaller loop and the flux will double. So now flux = 4F. Lets say that happened in 1s, so the average force per unit of charge is around (4F-2F)/1s = 2V. 
So the bigger loop will generate more force per unit of charge so a bigger current. 
In reality, when dealing with a magnet the larger loop wont double the flux when it gets closer, since the field of the magnet falls with 1/r³. But it will be something like 1.(some decimals) times bigger, but the point still the same. 
That's all.
