Physics

Problem

A particle of charge

q

and mass

m

enters a uniform magnetic field with speed

v

at an angle

\alpha

to the field direction. a. (i) Derive an expression for the pitch of the helical path in terms of the radius of the circular component and the angle

\alpha

. Show that

p = 2\pi r \cot\alpha

. b. (ii) A proton (

q = 1.6\times10^{-19}\,\text{C}

m = 1.67\times10^{-27}\,\text{kg}

) moves with speed

8.0\times10^{6}\,\text{m s}^{-1}

in a magnetic field of magnitude

0.050\,\text{T}

making an angle of

30^{\circ}

with the field direction. Using the expression derived in part (i), calculate the pitch of its path.