Відео

Thanks. Although having just watched it back, I don't know why I used Pythagoras rather than just saying x=3r cos45. Maybe my attachment to Greek geometry is stronger than I realised.

That is very nice of you to say so, thank you. I'm glad you found it useful. I'm uploading 2021 PAT today and should be up to date with 2022 and 2023 by early next week.

@@BlakeTerrorPhysics excellent!

Thank you for saying that, it's nice to know that someone finds it useful. There is plenty more content on the way - I'm about 30% through the physics videos, then I'll be doing maths and coding.

@@BlakeTerrorPhysics I have those subjects as well. I await your videos.

Yes, that's right. It's a combination of Kirchhoff's second law (i.e. the voltage one) and the symmetry of the circuit. Alternatively, once you see that there is no potential difference across d, it is evident that c is the same as b.

@@BlakeTerrorPhysics Alright, thank you!

Think of it in terms of density. We split the sphere into disks. Each disk has mass dm and volume dv. The disks and the sphere must have the same density, so mass divided by volume is the same for both. This means dm/dv=Mass of sphere/volume of sphere. So dm =M dv/volume of sphere.