Quick EMF question – Spherical Shell- North/South Pole, Equator

The question is: a conducting spherical shell of radius a rotates about the z axis with angular velocity ω, in a uniform magnetic field B= B[itex]_{0}[/itex][itex]\hat{z}[/itex] . Find an expression for the EMF developed between:

i) the north pole and the equator (2 marks);
ii) the north pole and the south pole (1 mark).

I’m struggling picturing why there is 0 flux between the north pole and south pole and a non-zero flux between the north pole and the equator.

So first of all, by rotates about the z-axis, I interpret this as any axis passing through the centre of the sphere.

I have attached two diagrams, the first i take the north and south pole to be aligned with the z axis (vertical) and the second the north and south aligned horizontally.

– From the first diagram, I think, I undertand the flux comments above, but in the second diagram , I would get zero flux for both cases…


– So by north and south pole do we mean north and south with respect to the z-axis, as the object is spherically symetric so otherwise how do you choose?
– I can also see that I have not used the fact that the object is a shell and not a dense sphere. Am I correct in thinking that the answers to i and ii remain unchanged if I were to replace the spherical shell with a sphere?

Many Thanks in advance for your assistance !

Attached Images
File Type: png flux2.png (2.7 KB)
File Type: png FLUX1.png (3.7 KB)


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