A particle of charge and mass enters a uniform magnetic field with speed at an angle…

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

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. (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

. (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.