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A metal disc of radius a=25cm rotates with a constant angular velocity ω=130 rad/s about its axis. Find the potential difference between the rim and the centre of the disc if the external magnetic field is absent
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1 Answers
24Here emf is induced due to motion of electrons about axis within disc
Consider an electron (mass m) ,at distance r (variable) from axis .
Fc=mω2r
Since no magnetic field =>reqd centripetal force will be provided by electric field(E)
=> Eq=mω2r q=charge of electron
=> E=mω2rq
Potentail difference=Vout-Vcenter=-∫E.dr
since E is directed outwards(radially) and dr is also taken radially outwards => dot product of vectors positive
=>Vout-Vcenter=-∫Edr
=>Vcenter-Vout=∫Edr=∫mω2rq dr
=>ΔV=\int _{0}^{R} \frac {m\omega ^2 r}{q}dr
=>\Delta V=\frac {m \omega ^2 R^2}{2q}
Now put the values to get answer[1]
