Answer to Question #99606 in Electricity and Magnetism for Ali hamza

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

According to Newton's second law, from the equilibrium between the centripetal force and the Lorentz force calculate the radii of the orbits:

$$qvB=m\frac{v^2}{r},\\ \space\\ r=\frac{mv}{qB}.$$

For the first and the second atom it gives respectively

$$r_1=0.104 \text{ m},\\ r_2=0.208\text{ m}.$$

For the situation shown in the figure the separation will be

$$d=2(r_2-r_1)=0.208\text{ m}.$$