I was wondering ,that why in the presence of uniform electric field the electrons are moving in a curved path.
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Have you tried looking at the forces involved and solving the two differential equations (one for $x$ and one for $y$)? – Kyle Kanos Jul 01 '15 at 13:05
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2It is the same as a thrown rock following a curved path in a uniform gravitational field. – mmesser314 Jul 01 '15 at 13:37
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The alternative to moving in a curved path is moving in a straight path. Which your electron will only do only if all the forces are parallel to its velocity vector. So an electron starting from rest in a uniform electric field will travel in a straight line - but that is an exception, not the rule. But you could think of that as a "curved path with infinite radius of curvature".
Floris
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Yes. To add on to this and help visualise it, the electrons will only accelerate in a straight line path if they are projected into the uniform electric field along the direction of the field lines. Notice, I am using the word accelerate in italics because if we look at the equation for the electrons path in a uniform field the nature of such an equation (being an x^2 equation means it is parabolic, and as such y is proportional to x^2) the direction along which is the Y-axis (at right angles to the field lines) it is at constant velocity, wheras parralel to the field lines it is accelerat – Jam Jul 01 '15 at 13:39
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...ing. (whoops, should watch the character count next time). So perpendicularly (to the field lines) it will be accelerating due to the change in direction. – Jam Jul 01 '15 at 13:40
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The electrons are not moving in a curved path. They are moving according to the solutions of the Newton's equation $$ m\textbf{a}=\textbf{F}(\textbf{r},\textbf{r}')=q\,\textbf{E}(\textbf{r},\textbf{r}') $$ As the above being a Cauchy problem, the form of its general solution explicitly depends on the initial conditions for position and velocity and in general the only way that can give back a straight line is that the particle is starting at rest and the force is constant. But these considerations are true for all mechanical systems, not only for electrons in an electric field.
gented
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