Question

An electron moving with a constant velocity \(v\) along X-axis enters a uniform electric field applied along Y-axis. Then the electron moves

• A. with uniform acceleration along Y-axis
• B. without any acceleration along Y-axis
• C. in a trajectory represented as \(y = ax^2\)
• D. in a trajectory represented as \(y = ax\)
• E. with uniform deceleration along X-axis

Hint:

Charged particle in perpendicular electric field behaves like projectile motion.

Answer 1

The Correct Option is A

Concept: Electric field exerts force: \[ F = qE \Rightarrow a = \frac{qE}{m} \]

Step 1: Motion along X-axis. No force along X → velocity remains constant.

Step 2: Motion along Y-axis. Constant electric field → constant force → uniform acceleration.

Step 3: Combine motions. Uniform motion in X + uniformly accelerated motion in Y → projectile motion.

Step 4: Trajectory equation. \[ y \propto x^2 \]

Step 5: Conclusion. Correct answers: (A) and (C)