A particle of charge and mass enters a uniform magnetic field of magnitude with a speed of

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A particle of charge

+2e

and mass

6.64\times10^{-27}\,\text{kg}

enters a uniform magnetic field of magnitude

0.10\,\text T

with a speed of

1.0\times10^{7}\,\text{m s}^{-1}

. The velocity vector makes an angle of

45^{\circ}

with the magnetic field direction. (i) Resolve the initial velocity into components parallel (

v_{\parallel}

) and perpendicular (

v_{\perp}

) to the magnetic field. (ii) Calculate the radius of the resulting helical path. (iii) Determine the pitch (linear distance parallel to

\mathbf B

travelled during one complete turn) of the helix. (iv) If the particle travels a distance of

0.20\,\text m

along the field direction, find the number of complete turns it makes in this distance.