Acceleration of a Charged Particle Between Two Points in an Electric Field

When a charged particle is placed in an electric field, it experiences a force that causes it to accelerate. The work done by the field on the particle changes its kinetic energy, allowing us to calculate its final velocity or time taken to travel between two points.

Key Idea: An electric field can do work on a charge and change its speed. A magnetic field, in contrast, only changes the direction of a moving charge — it never changes its speed.

Step 1 - Force on the charge:

Step 2 - Acceleration produced:

Step 3 - Work done in moving from A to B:

Step 4 - Work-Energy Theorem (work equals change in kinetic energy):

Step 5 - If the particle starts from rest (u = 0):

Step 6 - Time taken to travel distance d (starting from rest):

Given: 10¹⁰ electrons accelerated through a potential difference of 2000 V.

Find: Total energy gained.

Solution:

Answer: 3.2 × 10⁻⁶ J = 3.2 µJ

Given: An electron accelerated through a potential difference of 10⁵ V, starting from rest.
Find: Maximum speed attained.
Solution: Using v = \[\sqrt {2qV/m}\]​ with q = 1.6 × 10⁻¹⁹ C, m = 9.1 × 10⁻³¹ kg
Answer: v ≈ 1.87 × 10⁸ m/s

Think of potential difference like height on a hill. A ball released at the top (higher potential) rolls down to the bottom (lower potential), gaining speed as it goes.
Similarly, a positive charge "rolls down" the potential slope from high potential (A) to low potential (B), gaining kinetic energy along the way.