A cylindrical thin shell with length L, radius R and surface charge density ? ro

Question

A cylindrical thin shell with length L, radius R and surface charge density ? ro

A cylindrical thin shell with length L, radius R and surface charge density sigma rotates about its axis with angular velocity w which increases with time as w=kt where k is a constant and t greaterthanorequalto 0. The cylinder is very long (e.g. so you neglect fringing effects). (a) Find the magnetic field inside the cylinder (b) Find the electric field inside the cylinder (c) Find the total electric and magnetic field energy inside the cylinder.

Explanation / Answer

a) effective current i = sigma*L*2piR/(2pi/w)

= sigma LRw

magnetic field = uoi/2R

= uo*sigma LRw/(2R)

= 0.5 uo*sigma Lkt

b) Electric field inside cylinder = 0

c) total magnetic energy = (B^2/2uo)*piR^2L

= (0.5 uo*sigma Lw)^2/2uo* piR^2L

= uo*sigma^2*L^3*w^2*piR^2

totale electric field energy = 0

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