A proton projected in a magnetic field of 0.020 T travels along a helical path of radius 5.0 cm and pitch 20 cm. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton` =1.6X10^(-27)`kg.

Answer

`1*2xx10^5ms^-1`, `7*6xx10^4ms^-1`

Explanation

Here, `B=0*02T, r=6xx10^-2m`,
pitch `=24xx10^-2m`
Let `v_1` be the component of velocity of proton perpendicular to magnetic field. Then
`r=(mv_1)/(qB)` or `v_1=(rqB)/(m)`
`:. v_1=((6xx10^-2)xx(1*6xx10^(-19))xx0*02)/(1*6xx10^(-27))`
`=1*2xx10^5ms^-1`
Time period of revolution,
`T=(2pir)/(v_1)=(2pixx5xx10^-2)/(1*2xx10^5)=pixx10^-6s`
Let `v_2` be the component of velocity of proton along the direction of magnetic field. Then
`v_2=("pitch")/("time period")=(24xx10^-2)/(pixx10^-6)`
`=7*6xx10^4ms^-1`