2 Consider the same vortex filament as in Problem 5.1. Consider also a straight line through the center of the loop, perpendicular to the plane of the loop. Let A be the distance along this line, measured from the plane of the loop. Obtain an expression for the velocity at distance A on the line, as induced by the vortex filament.

The expression for the velocity at distance A on the line is

Explanation:

The free body diagram of the circular voltage filament is shown on the first uploaded image

Looking at the diagram we see that a straight pass through the center of the loop and this line is perpendicular to the plane of the loop

    R is the radius of this vortex filament ,   denoted the strength of the vortex filament , V is  the velocity that is been induce due to the distance A traveled, is the elemental length of the vortex filament

   Now the velocity that is been induced perpendicular to the plane of the loop  According to Biot-Sarvart law is  mathematically represented as

Now the velocity induced at the distance A on the line is mathematically represented as

This is  because   from the diagram applying Pythagoras theorem  

This is  because    from the diagram applying SOHCAHTOA            

12000j is work done

hello, i am papaguy.

i have found an answer to your question but use it as information.

information: because weak acids/bases have low concentration of hydrogen ions, the addition of water has a large impact on the ph. 2. a difference in 1 unit is a 10x difference in concentration for example; a liquid with ph of 3 is 10x more acidic than a liquid with a ph of 4. therefore, a liquid with a ph of 3 is stronger.

best of luck!