Question: On Wikipedia, it is stated that the Biot-Savart law is a formula used for determining the magnetic field pseudovector **B**(**r**) at a position vector **r** due to a current-carrying wire, but that the formula only works for constant/steady electric currents. Wikipedia then states the law:

[![enter image description here](https://i.stack.imgur.com/FqA1d.png)](https://i.stack.imgur.com/FqA1d.png)

So my question then is, if the magnetostatic assumption is employed, would it be okay to factor that current term $I$ out of the line integral? And if it is legitimate, why do most textbooks leave it in the integrand? Is there some hidden benefit to doing so?

Answer: 
Due to the physiology of the human arm, it's very difficult to throw an object much faster than 100mph. No matter what object is being thrown, it can't move faster than the hand that's holding it, so around 100mph is the upper speed limit of any thrown object.

A bow gets around this by using the elastic potential of the bow to store energy over an arbitrary period of time, rather than by trying to accelerate to maximum speed over the space of your arm's rotation. You can slowly and steadily pull back on the bow, storing more energy than you could have imparted with a throw. This allows arrows launched from a bow to reach 150mph or more. Since kinetic energy is proportional to the square of velocity, increasing speed by 50% more than doubles the amount of energy carried.
When an archer pulls back on a bow, it is the bow that bends. The energy that is able to be stored and released depends a lot on by the elasticity and tensile strength of the bow, and also the size of the bow, as that determines how much advantage you can get from leverage.

Leverage I would say is one of the main issues here.

Due to the length of the string, the archer has leverage over the ends of the bow, and is able to convert more of their own strength into the tensile material and therefore the propulsion of the arrow than they would by just throwing the arrow.

I'm not sure how to word it right, but I think there is also something to do around the concept that more strength can be used when there is more resistance/potential for inertia. Consider how it is easier to throw a palm-sized rock further than a small pebble, or a javelin further than an arrow

![enter image description here](https://i.stack.imgur.com/4wDFt.gif)

<https://science.howstuffworks.com/crossbow2.htm>