A particle with a charge q and a mass m passes through a region of a uniform electric field of length d in time t. The velocity v of a particle entering the field is directed along the field. Determine the electric field intensity.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#7.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>

    <p>
      $7.1.3$
      A particle with a charge $q$ and a mass $m$ passes through a region of a uniform electric field of length $d$ in time $t$. The velocity $v$ of a particle entering the field is directed along the field. Determine the electric field intensity.      
    </p>

    <h3>Solution</h3>
    <p>
      The motion of particle is accelerated by electric field, so
      $$d = vt-\frac{at^2}{2} \\;(1)$$
      Applying Newton Second Law
      $$F = qE = ma$$
      then,
      $$a = \frac{qE}{m} \\;(2)$$
      Putting $(2)$ into $(1)$
      $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$
    </p>
    <p style="text-align: right; font-style: italic; font-size: 14;">   
      BSc. Luis Daniel Fernández Quintana<br>
      Physics Department (FCNE)<br>
      Universidad de Oriente, Cuba<br>
    </p>



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