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The region between x=0 and x=L is filled...

The region between `x=0` and `x=L` is filled with uniform steady magnetic field `B_0hatk`. A particle of mass m, positive charge q and velocity `v_0hati` travels along x-axis and enters the region of the magnetic field. Neglect the gravity throughout the question.
a. Find the value of `l` if the particle emerges from the region of magnetic field with its final velocilty at an angel `30^@` to its initial velocity.
b. Find the final velocity of the particle and the time spent by it in the magnetic field, if themagnetic field now extends upto 2.1`L`.

Text Solution

Verified by Experts

a. `theta=30^@`
`sintheta=L/R`
`Here, R=(mv_0)/(B_0q)`

`:. Sin30^@=L/((mv_0)/(B_0q))`
`=1/2 = (B_0qL)/(mv_0)`
`:. L=(mv_0)/(2B_0q)`
b. In part a.
`sin30^@ =L/R or 1/2=L/R`
`or L=R/2`

Now when `L'=2.1L`
or `2.1/2Rimplies L'gtR`
therefore devistion of the particle is `theta=180^@` as shown in figure
`:. v_f=v_0hati`
and `t_(AB)=T/2=(pim)/(B_0q)`
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