A long thin non-conducting cylindrical pipe having surface charge density ‘sigma’, radius ‘R’ rotating with angular velocity omega = kt about is axis, where k is a positive constant. Which of the following statement is/are correct for inside region of pipe?
(A) Magnetic and electric field are uniform throughout region and do not vary with time
(B) Magnetic field is constant throughout region but vary with time and electric field is not constant throughout region and independent of time
(C) Magnetic field is not constant throughout region but independent of time and electric field is constant throughout region and vary with time
(D) Energy density (u) due to magnetic field varies with time as u = bt2 . (Where b is positive constant)

Dear Student,

Surface Charge Density=σRadius =RCharge per unit length of cylinder, q=σ×πR2For Magnetic field:Effective current through sruface of unit length of cylinder =qt=q2π/ω=qω2π=σπR2ω2πSo, Current I ωWe know that: Magnetic field inside any current carrying ring or cylinder, B  ISince,  Iω. Hence, B ω. Also, ω=kt. So, B t.For Electric field:Here, Net charge is constant and uniform on pipe. Charge is not changing with time.So, Electric field at any point inside pipe will also independent of time as there is no effect of moving charges on electric field. From above two arguments, Option B is correct.For Energy Density:Energy Density u=12εoE2+12B2μo=0+B22μouB2. But, B t.Hence, ut2 Option D is correct.

Answer is B and D.


  • 1
What are you looking for?