An electron accelerated by a potnetial difference `V = 1.0 kV` moves in a unifrom magentic field at angle `alpha = 30^(@)` to the vector `B` whose modulus is `B = 29 mT`. Find the pithch of the helical trajectroy of the electron.

Explanation

`T = eV = (1)/(2) mv^(2)`
(The given potential difference is not large enough to cause significant deviations from the nonletivistic formula).
Thus,. `v = sqrt((2eV)/(m))`
So, `v_(|\|) = sqrt((2eV)/(m)) cos alpha, v_(_|_) = sqrt((2eV)/(m)) sin alpha`
Now, `(m v_(_|_)^(2))/(r) = B ev_(_|_)` or, `r = (m v_(_|_))/(Be)`,
and `T = (2pi)/(v_(_|_)) = (2pi m)/(Be)`
Pitch `p = v_(|\|) T = (2pi m)/(Be) sqrt((2eV)/(m)) cos alpha = 2pi sqrt((2mV)/(eB^(2))) cos alpha`