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Q.

A wide, very long, insulating belt has a uniform positive charge per unit area σ on its outer surface. Rollers at each end starts rotating from rest with variable angular acceleration, α=at2+bt+c. Where a, b, c are constants and t is time elapsed from the starting of the motion. There is no slipping between the belt and the rollers. The radii of the rollers is r and the length of the belt is L. r<<L. The magnitudes of magnetic field at P (a point in between the belts) and Q (a point outside and close to the belt) as shown int the diagram at a time t respectively are neglect the edge effect ie., the length of the belt which is contact with pulley.

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a

(0, 0)

b

μ0rσ6(2at3+3bt2+6ct),0

c

μ0rσ3(2at3+3bt2+ct),μ0rσ9(2at3+3bt2+ct)

d

0,μ0rσ12(2at3+3bt2+ct)

answer is B.

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Detailed Solution

It behaves as two current carrying sheets carrying currents in the opposite directions.  At P the fields Are in the same direction and at Q they are in the opposite directions. Ampere’s law gives 

B=12μ0k;k=Current per unit width

k=1×νπ=σ[rω]

0ωdω=0t(at2+bt+c)dt

ν=rω 

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