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a metal disc of radius R rotates with an angular velocity omega about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. the induced emf betwen the rim and the axis of the disc is

a metal disc of radius R rotates with an angular velocity omega about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. the induced emf betwen the rim and the axis of the disc is 

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Imagine any radial line (from centre) drawn on the disc representing a wire that rotates .. the emf across this rotating wire has the same emf across it's ends as the disc would between it's rim and the centre ..  

The rate area is swept by this conductor .. dA/dt = πR² / rotation time 
time for 1 rotation = 2π rad(1rev) / ω rad/s .. .. t = 2π/ω (s) 

dA/dt = πR² / (2π/ω) = R²ω/2 .. (m²/s) 

From Faraday's law for electromagnetic induction .. emf E = (-) B x dA/dt 

.. ►E = (-) R²ωB / 2 .. .. (Volt)

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