Physics

Problem

Two singly ionised particles A and B enter the same uniform magnetic field with their velocities perpendicular to the field. Particle A has mass

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

and speed

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

, while particle B has mass

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

and speed

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

. a. (i) Show that the ratio of their orbital radii

r_A : r_B

equals the ratio

(m_A v_A) : (m_B v_B)

. b. (ii) Hence calculate the individual radii of their paths when the magnetic field magnitude is

0.25\,\text{T}

. c. (iii) Which particle completes more revolutions per second and by what factor?