a line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non- conducting spokes and is free to rotate without friction about its axis . a uniform magnetic field extends over a circular region within the rim. it is given by
B = -B°k (r ≤ A ,.. A < R )
= 0 (otherwise)
what is the angular velocity of the wheel after the field is suddenly switched off ?
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UP 0 DOWN 0 0 2
2 Answers
Let E be induced electric field..
dΦ = ∫E.dl
dt
πA2dB/dt=∫E.dl
By symmetry E is same on circumference..
so
πA2dB/dt=E.∫dl
Ï€A2dB/dt=E.2Ï€R
E=A2 dB
2R dt
force on charge rim = A2 dB λ2πR
2R dt
F=A2 dB λπ
dt
τ=A2 dB λπR
dt
MR2α=A2 dB λπR
dt
α=A2 dB λπ
dt MR
ω=α dt
ω=A2dBλπ/MR
dB=B0 as finally B=0 and initially B=B0
so
ω=A2B0λπ/MR..
find direction physically... as i have not taken care of ± signs [3]