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

Hint:

Charged particle in uniform electric field behaves like projectile motion.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
An electric field exerts a constant force on a charged particle (\( \vec{F} = q\vec{E} \)). If the initial velocity is not parallel or antiparallel to the force, the motion is analogous to projectile motion under gravity.
: Detailed Explanation:
Let the electric field \( \vec{E} \) be along the x-axis.
The force on the electron is \( \vec{F} = -e\vec{E} \), which is constant in magnitude and direction.
This gives the electron a constant acceleration \( a = eE/m \) along the x-axis.
If the initial velocity \( \vec{v} \) has a component perpendicular to the field (say along the y-axis), then:
- \( v_y \) remains constant (no force along y).
- \( v_x \) changes at a constant rate due to \( a \).
This combination of constant horizontal velocity and constant vertical acceleration (or vice-versa) results in a parabolic trajectory.
Step 3: Final Answer:
The path of the electron is a parabola.