Saved Bookmarks
| 1. |
Explain drift of electron and drift velocity. Derive equation of current in term of cross-section of conductor. |
|
Answer» Solution : `rArr` In conductor free electron collide with ions and direction of their motion is continuously changing. Let there be N electron in conductor (i = 1, 2, 3, ... , N). At given time velocity of ith electron be `v_(l)`then its AVEREGE speed `((1)/(N) sum_(i=1)^(N) v_(i) = 0 )`will be zero. `rArr ` When electric field is present then electron will be accelerated. `rArr` Acceleration of electron , `vec(a) = ("force " )/("MASS") = (- e vec(E))/(m)` which is for very short duration. `rArr `Charge of electron is ( - e) and mass be m. `rArr` Let last collision of `i^(th)` electron at time t. after this collision let `t_(i)` time is ELAPSED and after this velocity at time t be `vec(v_(t))` then, `vec(v_(t)) = vec(v_(i))` +at `THEREFORE vec(v_(t)) = 0 - (e vec(E))/(m) t "" [ because v_(i) = 0 ] `  `rArr` At time t average velocity of electron wi1l be average velocity of `v_(i)`velocity of all electron and it will be zero because `v_(i)`is zero for all electron. `rArr` Collision among electron not at definite interval hence direction of velocity of electron will be changing. `rArr` Let average time interval between two successive collision be `tau`which is called relaxation time `rArr` Average velocity of N electron gives drift velocity `vec(v_(d))` `therefore vec(v_(d)) = 0 - (e vec(E))/(m) . (t)_("average")` `therefore v_(d) = - (e vec(E))/(m) . tau` Which is called drift velocity of electron. |
|