Suppose an electron carrying charge e, moving along X-
axis is subjected to a uniform electric field of strength \(\vec E\) along Y-axis.
∴ Force on the electron,
\(\vec F= e\vec E\)
As the electron carries negative charge, force on it is in a direction opposite to \(\vec E\) (i.e. towards the positive plate).
Acceleration of electron
\(\vec α= \frac{force}{mass}= \frac{e\vec E}{m}\) .....................(1)
The electron moves under the combined action of its own uniform velocity (u) along X-axis and uniformly accelerated velocity along Y-axis due to the field.
At any time t, suppose the electron is at P(x,y).
Using
\(s=ut+\frac{1}{2}at^2\)
∴ x = ut ...................(2)
and y = \(\frac{1}{2}at^2\) ...................(3)
from eqn. (2), t = \(\frac{x}{u}\)
Putting in eqn. (3), we get
\(y= \frac{1}{2}a.\frac{x^2}{u^2}\)
\(y= \frac{1}{2}(\frac{eE}{m}).\frac{x^2}{u^2}\)
Clearly y ∝ x2
Thus, the path of charged particle is parabolic in nature.
