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An electron accelerated by a potential d...

An electron accelerated by a potential difference `V=1.0 kV` moves in a uniform magnetic field at an angle `alpha = 30^@` to the vector B whose modulus is `B=29 mT.` Find the pitch of the helical trajectory of the electron.

Text Solution

Verified by Experts

If v is the velocity of the electron then
`1/2mvV^(2)=eV`
`:.v=sqrt((2eV)/m)`
Pitch `=v cos alpha xx T=v cos alpha xx(2pi m)/(eB)`
`=(2pim)/(eB)=sqrt((2eV)/m)cos alpha`
`=2pi sqrt((2mV)/(eB^(2)))cos alpha`
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