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In the figure the wires AB and PQ carry constant current l_(1) and l_(2) respectively.PQ is of uniformly distributed mass m and length l.AB and PQ are both horizontal and kept in the same vertical plane.The PQ is in equilibrium at height h.Find (i) h in terms of I_(1),I_(2),l,m,g and other standard constants. (ii) If the wire PQ is displaced vertically by small distance prove that it performs SHM.Find its time period in terms of h and g. |
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Answer» Solution :(i) Magnetic repulsive force balances the weight . `(mu_(0)I_(1)I_(2))/(2pih)l mg rArr h=(mu_(0)I_(1)I_(2)l)/(2pimg)` (ii) Let the wire be displaced DOWNWARD by distance `x(LT lt h)`. Magnetic force on it will INCREASES, so it goes back towards its equilibrium position.Hence it performs oscillations. `F_(res)=(mu_(0)I_(1)I_(2))/(2x(h-x))l-mg` `=(mgh)/(h-x)-mg=(mg(h-h+x))/(h-x)` `=(mg)/(h-x)~=(mg)/hx "for"xltlt h` `:.T=2pisqrt(m/(mg//h))=2pisqrt(h/g)` |
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