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| <h3 id="back-link"><a href="../../#7.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#7.1">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| | | |
| <p> | | <p> |
| $7.1.3$ | | $7.1.3$ |
| 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. | | 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> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| The motion of particle is accelerated by electric field, so | | The motion of particle is accelerated by electric field, so |
| $$d = vt-\frac{at^2}{2} \;(1)$$ | | $$d = vt-\frac{at^2}{2} \;(1)$$ |
| Applying Newton Second Law | | Applying Newton Second Law |
| $$F = qE = ma$$ | | $$F = qE = ma$$ |
| then, | | then, |
| $$a = \frac{qE}{m} \;(2)$$ | | $$a = \frac{qE}{m} \;(2)$$ |
| Putting $(2)$ into $(1)$ | | Putting $(2)$ into $(1)$ |
| $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$ | | $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$ |
| </p> | | </p> |
| <p style="text-align: right; font-style: italic; font-size: 14;"> | | <p style="text-align: right; font-style: italic; font-size: 14;"> |
| BSc. Luis Daniel Fernández Quintana<br> | | BSc. Luis Daniel Fernández Quintana<br> |
| Physics Department (FCNE)<br> | | Physics Department (FCNE)<br> |
| Universidad de Oriente, Cuba<br> | | Universidad de Oriente, Cuba<br> |
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