Why is the magnetic flux density uniform at the center of the circular loop ?
It is not uniform. It varies in all directions. B is nearly uniform in the center of a long solenoid.
Magnetic field of a current loop:
For points in the plane of the loop, set x=0 and consider only Bx; Br=0.
As you move towards one part of the circumference you are moving away from another at 180° to the first. The rise from one tends to cancel the fall from the other, so the field is remarkably smooth and gently curved near the axis.
Thank you so much for you help , so its not uniform .... My textbook is really mistaken about almost everything >.< but what can I do .... You said that its nearly uniform at the center of the solenoid , so its not completely ? How so ?
thank you so much , that was really helpful !
Thank you so much , your simplified explanation was extremely helpful , thank you sincerely !
The attached screen dump shows two things. Firstly a circular loop of short filamentary segments, and secondly the B field measured across the circle, but very slightly offset from the plane of the circle which reduces the extreme peaks close to filaments.
If you want a 3D volume of reasonably uniform magnetic field you can use two plane loops in an arrangement called a Helmholtz coil. https://en.wikipedia.org/wiki/Helmholtz_coil
Thanks ، I think I understand now , thank you so much for the Helmholtz example ,realky helped
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