Saved Bookmarks
| 1. |
In Fig a rod of length l and mass m moves with an intial velocity u on a fixed frame containing inductor L and resistance R.PQ and MN are smooth conducting wires. There is auniform magnetic field of strength B. Initially, there is no current in the inductor. find the total cherge flows through the inductor by the time, velocity of rod becomes nu_(f) and the rod has travelled a distance x. |
Answer»  `(Bl nu)/(R ) = i_(2) RARR Bl nu = L(di_(1))/(dt)` `m(d nu)/(dt) = - IlB = - (i_(1) + (Bl nu)/(R )) lB` `rArr m int d nu = - lB int i_(1) dt - (B^(2)l^(2))/(R )int nu dt` `rArr m(nu_(f) - u) = - lBQ - (B^(2)l^(2))/(R ) x` `(nu_(f) =` velocity when it has moved a distance `x`) `rArr Q = ((-B^(2)l^(2))/(R) x - m(nu_(f) - u))/(Bl)` |
|