Answer to Question #99706 in Electricity and Magnetism for ak

Question

Two singly ionized atoms move out of a slit at point S, as shown in figure, and into a magnetic
field of magnitude 0.100 T pointing into the page. Each has a speed of 1.00 × 106 m s−1

. The nucleus of the
first atom contains one proton and has a mass of 1.67 × 10−27 kg, whereas the nucleus of the second atom
contains a proton and a neutron and has a mass of 3.34 × 10−27 kg. Find their distance of separation when
they strike a photographic plate at P.

Answer 1

If the plate is situated along the diameters of the particles' orbits, the separation simply will be the difference between their diameters. While moving in a magnetic field, a charged particle experiences a centripetal force and an electromagnetic force called after Lorentz:

$$\frac{mv^2}{R}=qvB,\\ \space\\R=\frac{mv}{qB},\\ \space\\ s=d_2-d_1=2R_2-2R_1=\\ \space\\=\frac{2v}{qB}(m_2-m_1)=0.208\text{ m}.$$