The region between ` x=o and x = L` is filled with uniform, steady magnetic field `B_(0) hat(k)`. A particle of mass `m` , positive charge `q` and velocity `v_(0) hat(i)` travels along ` x-axis` and enters the region of the magnetic field. Neglect gravity throughout the question .
(a) Find the value of `L` if the particle emerges from the region of magnetic field with its final velocity at angle `30^(@)` to its initial velocity.
(b) Find the velocity of the particle and the time spent by it in the magnetic field, if the magnetic field now extends upto `2.1L`.

Answer

(i) 2 (ii)1

Explanation

(i) 2 (ii 1

(i) `theta=30^(@)`
`sin thea=L/R`
Here `R=(mv_(0))/(B_(0)q):. sin 30^(2)=L/((mv_(0))/(B_(0)q)`
or `1/2=(B_(0)qL)/(mv_(0)):. L=(mv_(0))(2B_(0)q),` (ii) in part (i)

`sin 30^(@)=L/R` or `1/2=L/R` or `L=R//2`
Now when `L'=2.1L` or `2.1/2RimpliesL'gtR`
Therefore, deviation of the particle is `theta=180^(@)` as shown
`:.v_(f)=-v_(0)hati` and `t_(AB)=T//2=(pim)/(B_(0)q)`