Please help:

Asked by nitishkrnehu09 | 1st Jan, 2018, 04:14: AM

Expert Answer:

Force on cylinder due to ( il x B ) force F is B×i×l , where B is magnetic field , i is current passing through cylinder and l is the length of the cylinder.
 
This force gives a torque  τ to the cylinder which is given by τ = I × α, where I is moment of inertia and α is angular acceleration.
 
τ = F × R  = I×α 
 
I×α = (mR/ 2)×α = B×i×l×R
begin mathsize 12px style a n g u l a r space a c c e l e r a t i o n space space alpha space equals space fraction numerator 2 cross times B cross times i cross times l over denominator m cross times R end fraction
l i n e a r space a c c e l e r a t i o n space q space equals space alpha cross times R space equals space fraction numerator 2 cross times B cross times i cross times l over denominator m end fraction
a f t e r space t r a v e l l i n g space d i s tan c e space a space t h e space s p p e d space i s space v squared space equals space 2 cross times q cross times a space equals space fraction numerator 4 cross times B cross times i cross times l cross times a over denominator m end fraction
h e n c e space v space equals space square root of fraction numerator 4 cross times B cross times i cross times l cross times a over denominator m end fraction end root end style
 

Answered by  | 1st Jan, 2018, 03:13: PM