IIT JEE , AIEEE Forum - Physics , Magnetism

Avinash_Bhat

You know that the force ( F ) acting on a current ( I ) carrying conductor of length ( L ) of resistance ( R ) held in a magnetic field ( B ) is given by:

F = BIL ( conductor : perpendicular to magnetic field : perpendicular to direction of current ........... as per Fleming's Left Hand Rule )

Now to the important part of the question:

Let the mass of the inductor be M. Then the acceleration of the conductor A is given by: A = F / M

As soon as the conductor begins to move on account of this force, MOTIONAL EMF ( E ) comes into play, isn't it ???? So induced current ( i ) in the opposite direction of ( I ) { as per Fleming's left hand rule } should be : i = E / R = BLV / R. (Due to acceleration, V is increasing)

SO THIS SHOULD OPPOSE THE FORCE F AND HENCE THE MOTION OF THE CONDUCTOR....................................... THEREFORE THE FORCE ON THE CONDUCTOR GRADUALLY DECREASES ON AND ON BUT NEVER BECOMES ZERO.

IS THIS TRUE OR FALSE ??????????????

PLEASE EXPLAIN IF FALSE...................

pratyush.pande

False a teminal velocity will be reached if friction is absent

see u can get the velocity by itegrating the expression

the current as u say changes with the speed... the motional emf opposes the battery emf so if the emf of the batter is E

the net emf = E - Blv

hence the current = ( E - Blv)/R

and hence the force is = B*l* ( E - Blv)/r

so the acc= (EBl/rm) - B²l²v/rm

now as acc=dv/dt

we can integrate the above exp and get the exp for velocity

it comes out to be an exponential one like that of current decay in CR circuit...

so the velocity and hence the force becomes zero at infinite time.

but before that a teminal velocity is reached at which both forces balance each other and the net force is zero

hence B*l* ( E - Blv)/r =0

and v = E/Bl

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