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Let `y gt 0` be the region of space with a uniform and constant magnetic field `B hat(k)`. A particle with charge and mass m travels along the y-axis and enters in magnetic field at origin with speed `v_(0)` in region in particle is subjected to an additional friction force `vec(F)= - k vec(v)`. Assume that particle remains in region `y gt 0`.A. `x=(kmv_(0))/(k^(2)+(qB)^(2))`B. `x=(qBmv_(0))/(k^(2)+(qB)^(2))`C. `y=(kmv_(0))/(k^(2)+(qB)^(2))`D. `y=(qBmv_(0))/(k^(2)+(qB)^(2))` |
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Answer» Correct Answer - B::C `vec(F) = ma = -k (v_(x) hat(i) + v_(y) hat(j)) + q (v_(x)hat(i) + v_(y) hat(j)) xx B hat(k)` `ma_(x) = -kv_(x) + qv_(y) B` `ma_(y) = -kv_(y) - qv_(x)B` At `t = 0, v_(x) = 0" " v_(y) = v_(0) " " x = 0 " " y = 0` finally `v_(x) = 0 " " v_(x) = 0 " " x = x_(1) " " y = y_(1)` `m_(x)o = -kx_(1) - qx_(1) B` `rArr x_(1) = (qBmv_(0))/(k^(2) + (qB)^(2)) rArr y_(1) = (kmv_(0))/(k^(2) + (qB)^(2))` |
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