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Shows two long metal rails placed horizontally and parallel to each other at a separation i. A uniform magnetic field b exists in the vertically downward direction. A wire of mass m can slide on the rails. The rails are connected to a constant current source which drives a current I in the circuirt. The friction coefficient between the rails and the wire is `mu`. (a) What should be the minimum value of `mu` which can prevent the wire from sliding on the rails? (b) Describe the motion of the wire if the value of `mu` is half the value found in the previous part.

Text Solution

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(a) The force on the wire due to the magnetic field is
`vecF=iveclxxvecB or F=ilb`
It acts towards right in the figure provided. If the wire does not
slide on the rails, the force of friction by the rails should be
equal to F. If `mu_0` be the minimum coefficient of friction which
can prevent sliding, this force is equal to `mu_0mg`. Thus,
`mu_0mg=ilB or mu_0=(ilB)/(mg)`
(b) If the friction coefficient is `mu=(mu_0)/2=(ilB)/(2ng)`, the wire will
slide towards right. The frictional force by the rails is `f=mumg=(ilB)/2 towards left`
The resultant force is `ilB-(ilB)/2=(ilB)/2` towards right. The
accleration will be `a=(ilB)/(2m)`. The wire will slide towards`
right with this acceleration.
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