The arrangement shown is placed in a vertical uniform magnetic field. Two metal rods of length λ and masses m 1 and m 2 are pulled apart from rest by a constant force F. Find the current in the resistor R as a function of time.
Text Solution
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Sol. Let v 1 and v 2 be the instantaneous velocity force the rods m 1 and m 2 respectively. The emf's across the rod will be
E 1 = B λ v 1 and E 2 = B λ v 2
The instantaneous current is
I = 
.....(1)
The acceleration of each rod is given by
(v 1 + v 2 )
and 
(v 1 + v 2 )
Adding the above two equations,
(v 1 + v 2 ) = F 
.. (2)
Using equation (1), 
where μ = 
or 
On integrating, I = 
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