Question

If an electron has an initial velocity in a direction different from that of an electric field, The path of the electron is:
(A) a straight line
(B) a circle
(C ) an ellipse
(D) a parabola

Answer 1

Here consider a projectile motion. For this consider the initial velocity can be resolved into two components. One is along the direction of electric field and other perpendicular to electric field. When an object is thrown or projected in air, it depends only on the acceleration due to gravity and this is called projectile motion. The trajectory is the path followed by the particle. The path followed can be parabolic if only a constant acceleration is influenced by the vertical object of the particle.

Complete step by step solution:
Consider an electric field around a point charge and the direction of the electric field is in positive x direction. The initial velocity is in a direction that makes theta angle with the x-axis. Thus one component of velocity is parallel to the electric field and the other is perpendicular to the electric field. The parallel component of velocity increases and hence acceleration also increases.
$v=u+at$
where, v is the final velocity
u is the initial velocity
a is the acceleration
t is the time taken
Here $a=\dfrac{qE}{m}$
where, q is the charge
E is the electric field
and m is the mass
When an object is thrown or projected in air, it depends only on the acceleration due to gravity and this is called projectile motion. The trajectory is the path followed by the particle. The path followed can be parabolic if only a constant acceleration is influenced by the vertical object of the particle.
In a projectile motion, generally there will be two velocities. When the acceleration is perpendicular to velocity it will be a projectile motion Hence the path is parabola.
The velocity at the origin can be resolved into two components. One is along the direction of electric field and other perpendicular to electric field. Thus the resultant path is parabola.

Therefore, option (D) is correct.

Note:
In a projectile motion, generally there will be two velocities. When the acceleration is perpendicular to velocity it will be a projectile motion The initial velocity can be resolved into two components. One is along the direction of electric field and other perpendicular to electric field. Thus the resultant path is parabola.