Introduction

When charged particles enter electric fields, they experience forces that can dramatically alter their motion. Understanding these interactions is crucial for many applications in modern physics and technology, from particle accelerators to television displays.

Electric Fields Between Parallel Plates

A uniform electric field is created when two parallel conducting plates are connected to a voltage source. The strength of this electric field (E) is given by:

$E = \frac{V}{d}$

Where:

Forces on Charged Particles

When a charged particle enters an electric field, it experiences an electric force given by:

$F = qE$

Where:

This force causes acceleration according to Newton's Second Law:

$F = ma$

Therefore, the acceleration of the charged particle is:

$a = \frac{qE}{m}$

Trajectories in Electric Fields

When a charged particle enters an electric field with an initial velocity, its motion can be analyzed by breaking it down into two components:

This results in a parabolic trajectory, similar to projectile motion in gravitational fields.

Comparison with Gravitational Fields

Characteristic	Electric Fields	Gravitational Fields
Force Direction	Depends on charge polarity	Always attractive
Force Magnitude	$F = qE$	$F = mg$
Trajectory Shape	Parabolic	Parabolic
Acceleration	Usually larger	9.81 m/s² on Earth
Affected Objects	Only charged particles	All matter

Negligible Gravitational Effects

For charged particles, gravitational forces are typically negligible compared to electric forces. For example, an electron near Earth's surface experiences a gravitational force of:

$F_g = \frac{GMm}{r^2}$

$F_g = \frac{(6.67 \times 10^{-11})(6.0 \times 10^{24})(9.109 \times 10^{-31})}{(6.371 \times 10^6)^2}\\ = 9.0 \times 10^{-30} \text{ N}$

This is vastly smaller than typical electric forces on the same particle.