An electron gun `G` emits electons of energy `2 keV` travelling in the positive x-direction. The electons are required to hit the spot `S` where `GS=0.1 m`, and the line `GS` makes an angle of `60^@` with the x-axis as shown in figure. A uniform magnetic field `B` parallel to `GS` exists in the region outside the electron gun.

find the minimum value of `B` needed to make the electrons hit `S`.

Answer

A, D

Explanation

`t=1/(V cos 60), T=(2pim)/(qB)`
`nT=t`
`(n2pimV)/(qB)=0.2`
`(pinsqrt(2mE))/(qB)=0.1`
`B=(pinsqrt(2xx9xx10^(-31)xx2xx10^(3)xx1.6xx10^(-19)))/(exx0.1) rArrB=(pin)/0.1sqrt((36xx10^(-28))/(1.6xx10^(-19)))=(pin)/0.1sqrt((9xx10^(-6))/4)`
`B=15pinxx10^(-4)T rArr B_(min)=15pixx10^(-4)T`