Question

what magnetic field strength will allow the electron to pass between the plates without being deflected

Answer 1

Complete Question

An electron travels with speed 2.0 X 10^7 m/s between two parallel charged plates. The plates are separated by 2.0 cm and are charged by a 400V battery. What magnetic field strength and direction will allow the electron to pass between the plates without being deflected.?

Answer:

The value  $B = 0.001 \ T$

Explanation:

From the question we are told that

   The  speed of the electron is  $v = 2.0 *10^{7} \ m/s$

    The voltage  is  $V = 400 \ V$

     The distance of separation is  $d= 2.0 \ cm = 0.02 \ m$

Generally the electric field is mathematically represented as

       $E = \frac{V}{d }$

=>    $E = \frac{400}{0.02 }$

=>     $E = 20000 V/m$

Generally for the electron to pass without deflection then

     $F_B = F_E$

Where $F_B$ is the maximum magnetic force acting on the electron which is mathematically represented as

       $F_B = evBsin (\theta )$

Since we are considering maximum magnetic field then $\theta = 90^o$

=>   $F_B = evB$

And  

    $F_E$ is the electric force on the electron which is mathematically represented as

       $F_E = e * E$

Here e is the charge on the electron with the value $e = 1.60 *10^{-19} \ C$

=>   $F_E = 1.60*10^{-19} * 20000$

=>      $F_E = 3.2*10^{-15} \ N$

So

    $3.2*10^{-15} = q* v B$

=>    $B = \frac{3.2*10^{-15}}{ 2.0*10^7 * 1.6*10^{-19}}$

=>     $B = 0.001 \ T$