Question

An electron is moving with velocity \(v_0 \hat{i}\). If a uniform electric field \(\vec{E} = E_0 \hat{j}\) is set up in the region, the electron will:

• A. describe a circular path
• B. describe a helical path
• C. describe a parabolic path
• D. continue moving without any deviation

Hint:

Remember: Perpendicular Electric Field \(\rightarrow\) Parabolic path. Perpendicular Magnetic Field \(\rightarrow\) Circular path.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a charged particle enters a uniform electric field perpendicular to its initial velocity, it experiences a constant force in the direction of the field (or opposite, for negative charges). This is analogous to projectile motion in a gravitational field.

Step 2: Detailed Explanation:
1. The electron has initial velocity in the x-direction (\(v_x = v_0\)). 2. The electric field is in the y-direction (\(E_y = E_0\)). 3. The force on the electron is \(\vec{F} = -e\vec{E} = -eE_0 \hat{j}\). 4. This results in a constant acceleration in the y-direction (\(a_y = -eE_0/m\)) while the x-velocity remains constant. 5. The displacement \(x = v_0 t\) and \(y = \frac{1}{2} a_y t^2\). Combining these gives \(y \propto x^2\), which is the equation of a parabola.

Step 3: Final Answer:
The electron will describe a parabolic path.