1.

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). Assumethat particle remains in region y gt 0.

Answer»

`x=(kmv_(0))/(k^(2)+(qB)^(2))`
`x=(qBmv_(0))/(k^(2)+(qB)^(2))`
`y=(kmv_(0))/(k^(2)+(qB)^(2))`
`y=(qBmv_(0))/(k^(2)+(qB)^(2))`

Solution :`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`
`rArrx_(1) = (qBmv_(0))/(k^(2) + (qB)^(2)) rArr y_(1) = (kmv_(0))/(k^(2) + (qB)^(2))`


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