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.
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<h3> Statement </h3>
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$7.1.3$
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.
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<h3>Solution</h3>
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The motion of particle is accelerated by electric field, so
$$d = vt-\frac{at^2}{2} \quad(1)$$
Applying Newton Second Law
$$F = qE = ma$$
then,
$$a = \frac{qE}{m} \quad(2)$$
Putting $(2)$ into $(1)$
$$\boxed{E = 2m\frac{d-vt}{qt^2}}$$
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<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>
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