11.3 Motion of a charged particle in a magnetic field  (Page 3/6)

Strategy

1. The direction of the magnetic field is shown by the RHR-1. Your fingers point in the direction of v , and your thumb needs to point in the direction of the force, to the left. Therefore, since the alpha-particles are positively charged, the magnetic field must point down.
2. The period of the alpha-particle going around the circle is
   
   $T=\frac{2\pi m}{qB}.$
   
   Because the particle is only going around a quarter of a circle, we can take 0.25 times the period to find the time it takes to go around this path.

Solution

1. Let’s start by focusing on the alpha-particle entering the field near the bottom of the picture. First, point your thumb up the page. In order for your palm to open to the left where the centripetal force (and hence the magnetic force) points, your fingers need to change orientation until they point into the page. This is the direction of the applied magnetic field.
2. The period of the charged particle going around a circle is calculated by using the given mass, charge, and magnetic field in the problem. This works out to be
   
   $T=\frac{2\pi m}{qB}=\frac{2\pi \left(6.64\times {10}^{\mathrm{-27}}\text{kg}\right)}{\left(3.2\times {10}^{\mathrm{-19}}\text{C}\right)\left(0.050\text{T}\right)}=2.6\times {10}^{\mathrm{-6}}\text{s.}$
   
   However, for the given problem, the alpha-particle goes around a quarter of the circle, so the time it takes would be
   
   $t=0.25\times 2.61\times {10}^{\mathrm{-6}}\text{s}=6.5\times {10}^{\mathrm{-7}}\text{s.}$

Significance