A cylindrical shell of length L, radius R, and mass Mis uniformly charged on its surface with total chargeQ, and is rotating with an angular speed of about its axis which is oriented along the z-axis, as shown.a) Consider a horizontal thin ring-like region on the surface of shell with thickness dz, as shown andcalculate the infinitesimal current di due to the rotating charge on this ring, in terms of dz.b) Calculate the infinitesimal magnetic moment dụ due to this current.c) Calculate the infinitesimal magnetic field dB, on the z-axis of cylinder at the point P at the distanceof d above the center of cylinder (d>L/2).d)Integrate this dB over dz, to find the magnetic field B at point P. Also find B at very far away.e) Integrate du over dz, to find total magnetic momentu.f) Show that is related to the angular momentum of the rotating sphere. Show the relation.g) Use this to calculate the B filed at point P when this point is very far away (d>> L & R).X@0diPZdzy

Given: Point P at distance d from the center of cylinder.

A cylindrical shell of length L, radius R, and mass M is uniformly charged on its surface with total charge Q, and is rotating with an angular speed of about its axis which is oriented along the z-axis, as shown. a) Consider a horizontal thin ring-like region on the surface of shell with thickness dz, as shown and calculate the infinitesimal current di due to the rotating charge on this ring, in terms of dz. b) Calculate the infinitesimal magnetic moment du due to this current. c) Calculate the infinitesimal magnetic field dB, on the z-axis of cylinder at the point P at the distance of d above the center of cylinder (d>L/2). d) Integrate this dB over dz, to find the magnetic field B at point P. Also find B at very far away. e) Integrate du over dz, to find total magnetic momentu. f) Show that is related to the angular momentum of the rotating sphere. Show the relation. g) Use this u to calculate the B filed at point P when this point is very far away (d>> L & R).

A cylindrical shell of length L, radius R, and mass M is uniformly charged on its surface with total charge Q, and is rotating with an angular speed of about its axis which is oriented along the z-axis, as shown. a) Consider a horizontal thin ring-like region on the surface of shell with thickness dz, as shown and calculate the infinitesimal current di due to the rotating charge on this ring, in terms of dz. b) Calculate the infinitesimal magnetic moment du due to this current. c) Calculate the infinitesimal magnetic field dB, on the z-axis of cylinder at the point P at the distance of d above the center of cylinder (d>L/2). d) Integrate this dB over dz, to find the magnetic field B at point P. Also find B at very far away. e) Integrate du over dz, to find total magnetic momentu. f) Show that is related to the angular momentum of the rotating sphere. Show the relation. g) Use this u to calculate the B filed at point P when this point is very far away (d>> L & R).