Question

In a mass spectrometer, a single-charged particle (charge e) has a speed of 1.0 × 10 6 m/s and enters a uniform magnetic field of 0.20 T. The radius of the circular orbit is 0.020 m. What is the mass of the particle?

Answer 1

Answer:

The mass is  $m =6.4*10^{-28} \ kg$

Explanation:

From the question we are told that

   The  speed of the charge is  $v = 1.0 *10^{6} \ m/s$

    The  magnetic field is  $B = 0.20 \ T$

     The radius is $r = 0.02 \ m$

      The value of the charge is  $e = 1.60 *10^{-19} \ C$

The centripetal acting on the charge moving in the circular orbit is mathematically represented as

        $F_c = \frac{mv^2}{r }$

Now this centripetal force is due to the force exerted on the charge by the magnetic field on the charge which is mathematically represented as

     $F_m = qv B sin\theta$

At the maximum of this magnetic force $\theta = 90 ^o$

So  

     $F_m = e v B sin(90)$

      $F_m = e v B$

Now given that it is this  magnetic force that is causing the circular motion we have that

       $F_c = F_m$

=>     $\frac{mv^2}{r } = ev B$

=>     $m = \frac{e * B * r }{v }$

substituting values

       $m = \frac{ 1.60 *10^{-19} * 0.20 * 0.020 }{1.0*10^{6} }$

     $m =6.4*10^{-28} \ kg$