Motion of a Charged Particle?

📌 CONCEPT: A charged particle moving in a uniform electric field will experience a constant force due to the electric field, causing it to change its direction and speed.

📐 RULE / FORMULA: According to the equation F = qE, the force on a charged particle is directly proportional to the magnitude of the electric field (E). Therefore, if the electric field is increased by a factor of 4, the force on the particle will also increase by a factor of 4.

💡 WORKED EXAMPLE: Suppose a particle of charge +q moves in an electric field E with a force F = qE. If the electric field is doubled (E' = 2E), the new force F' = qE' = q(2E) = 2qE, which is twice the original force. The particle will change its path and accelerate in the same direction as the electric field.

⚠️ COMMON MISTAKE: Students often confuse the direction of the force on a charged particle in an electric field, thinking that the force is always opposite to the direction of the electric field. However, the direction of the force is actually given by the equation F = q(E or -E), where the direction is determined by the sign of the charge and the direction of the electric field.