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On an inclined plane, two conducting rai...

On an inclined plane, two conducting rails are fixed along the line of greatest slope. A conducting rod AB is placed on the radils so that it is horizontal. A vertically upward uniform magnetic field is present in the region. A current i flows through AB from B to A. The mass of AB is m and the coefficient of friction between the rod and rails is `mu`. Find the minimum and maximum value of B, so that the rod can stay in equilibrium. Assume that `mu lt tan theta`

Text Solution

Verified by Experts

`B_("min") = (mg (sin theta - mu cos theta))/(lL (cos theta + mu sin theta))`
`B_("max") = (mg (sin theta + mu cos theta))/(IL (cos theta - mu sin theta))`
For equilibrium `B_("min") le B le B_("max")`
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