Doubt from Electrostats and Magnetism

In Q2 I'm unable to identify at what angle will it enter region a≤z<b

Find velocity magnitude by energy conservation (electric field along k direction does work)

And then to completely reverse direction the distance equals to radius of the circle.

Sry for inverted image

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Why did you assume the final velocity in the k direction though?

All the forces that acts both magnetic and electric such a way that it only produces velocity in y-z plane... check it

Yeah buy why no component of velocity along y axis?

Yes there is component diagram has velocity v in y z plane (so you can take components)
Also it does planar motion only in y z plane

And why haven't you considered work due to y component of electric field?

W by magnetic will be 0 but due to electric field along why there shall be some work and moves in y also!

Yes I haven’t noticed that!
Yeah then my whole solution is wrong !because I don’t know the displacement along y axis.

Pls ignore post #2

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I think the work done in y-direction should be zero in order to obtain minimum value of b because radius of circular path will be minimum when v is minimum which is at y=0.

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Well i think that's not the explaination. Acc to me better explaination would be if there's some y component of velocity then it will reverse back at some angle and finally the path would never be reversed. We can completely reverse path only in the case where Fmagnetic and Felectric along y cancel each other i.e. no component of velocity in y.