ncert ques

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a line charge Î» 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_Â°k (r â‰¤ A ,.. A < R )
= 0 (otherwise)
what is the angular velocity of the wheel after the field is suddenly switched off ?

#Physics #Electricity and magnetism

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2 Answers

33

Abhishek Priyam ·2009-02-14 08:36:04

Let E be induced electric field..

dÎ¦ = âˆ«E.dl
dt

Ï€A²dB/dt=âˆ«E.dl

By symmetry E is same on circumference..
so
Ï€A²dB/dt=E.âˆ«dl
Ï€A²dB/dt=E.2Ï€R

E=A² dB
2R dt

force on charge rim = A² dB Î»2Ï€R
2R dt

F=A² dB Î»Ï€
dt
Ï„=A² dB Î»Ï€R
dt

MR²Î±=A² dB Î»Ï€R
dt
Î±=A² dB Î»Ï€
dt MR
Ï‰=Î± dt

Ï‰=A²dBÎ»Ï€/MR

dB=B₀ as finally B=0 and initially B=B₀

so
Ï‰=A²B₀Î»Ï€/MR..

find direction physically... as i have not taken care of Â± signs [3]

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62

Lokesh Verma ·2009-02-14 21:22:12

good work priyam :)

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