Magnetic Field Above a Square Loop

Physics Ninja calculates the magnetic field produced by a square loop. The field is calculated at a point above the center of the loop. Symmetry of the problem is used to simplify the calculations and trigonometric substitution is used to simplify the integral.

[mariahhasfuntimeshere]

Thank you so much for this!!! Normally I have a studio class to do this problem where I can ask questions and work in a group, but school has gone online and this is a huge help!

[amiyancandol]

I derived a general formula for this:

[Omeruy]

Sir thank you very much this helped me a lot. I used to try to memorize that complicated integral that also encounter in the eletric field calculations. Greetings

[vishakhasasuke]

Thanks a lot for this. This derivation is of great help for my research project on Square Helmholtz Coils. 😭❤️

[anandannapurna]

I solved this before seeing your video a I checked, got the same answer.
😊

[mina]

Thank you so much
That really helped❤️

[yibowang]

Subscribed! What more challenging is to calculate the magnetic flux on another loop antenna, then we need to integral the dS, can you do it?

[mazinshamshad]

Sir why are you using x prime instead of just simply writing x?

[amiyancandol]

Hey found you again! But I got answer half of this, in denominator why is it 2π not 4π

[tamuno-omiegogo]

Hi, Thanks for your time trying to decimate the problem with your solution. My question is, "What if P is away from the origin" could you please provide a hint? Thanks

[serdaryavuz]

Thanks for the video its very helpful !
If I was flowing clockwise would there be changes ?

[JuanhongHai]

I have one doubt toward your work, when it comes to the simplification of trigonometrics, I saw that in the 17:50 section of the video, why you simplify into 1/(a^2) rather than 1/a? Could you please interpret a bit? Thank you very much!

[shiranbarbalat]

hey! you are the best:) its possible to solve this problem with amper law?

[gvincent]

sir, could you do this for isosceles trapezium . using same cooncept.
please

[Harmonicanalysis]

I've seen certain formulas for magnetic field that have the denominator set as r squared instead of r cubed? What's the difference between the two and when would you know when to apply which

[diegonavia]

does someone know how to integrate this result to obtain the expression of a very large solenoid of square loops

[cosmolearner]

Whether the same illustration can be solved by the Ampere's law...?

[ryanlee]

at 15:34 how is the distance from the wire a when we know the z axis is a distance a/2 away

[mariahhasfuntimeshere]

Is it possible to use the definition of a cross product and then the opposite side over the hypotenuse?

[srisidvicious]

Excellent explanation. Can I ask what the field at the center of an infinitely long square solenoid would be? Is it simply 2sqrt(2)*mu*I*(N)/(Pi*a) where N = turns/meter?