A singly-ionised proton is projected perpendicular to a uniform magnetic field.

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

Problem

A singly-ionised proton is projected perpendicular to a uniform magnetic field. (i) Derive an expression for the radius

r

of the circular path in terms of the particle’s mass

m

, speed

v

, charge

q

and the magnetic field

B

. (ii) From this result, obtain an expression for the time period

T

of one full revolution of the proton. (iii) Using

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

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

v=3.0\times10^{6}\,\text{m s}^{-1}

and

B=0.20\,\text T

, calculate (a) the radius of the path and (b) the time period of revolution.