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A conductor (rod) of mass m, length l ca...

A conductor (rod) of mass m, length `l` carrying a current i is subjected to a magnetic field of induction B. If the coefficients of friction between the conducting rod and rail is `mu,` find the value of I if the rod starts sliding.

Text Solution

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The magnetic force is `F_m=ilB sinvarphi`,
where `varphi_B` =Angle between current and magnetic field =`90^@`.
or `F_m=ilB`
but it acts at an angle `theta` with horizontal as shown in Fig. according to Fleming's left hand rule.
Then the net force along x- and y-axis are
`F_y=N-(mg+F_m sin theta)=0`
or `N=mg+F_msin theta`....(i)
`F_x=f-F_m cos theta=0`....(ii)
or `f=F_m cos theta`
Law of friction, `f=muN`....(iii)
By using the above equations
`mu(mg+F_msin theta)=F_m cos theta`
or `F_m=(mumg)/(cos theta-musin theta) or ilB=(mumg)/(cos theta-musin theta)`
or `i=(mumg)/(lB(cos theta-musin theta))`
.
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