Determining Particle Charge for Stationary State in an Electric Field

In this article, we will explore the process of finding the charge and magnitude required for a particle to remain stationary in an electric field.

Introduction

When a particle is placed in an electric field, external forces such as the gravitational force can affect its motion. To keep the particle in a stationary state, the electrical force and the gravitational force must be balanced. This article demonstrates the method to determine these forces and the necessary charge.

Given Information

Mass of the particle: 1 gram (0.001 kg) Electric field strength: 160 N/C Acceleration due to gravity: 9.8 m/s2

Step-by-Step Calculation

The gravitational force acting on the particle can be calculated using the formula:

Fg m middot; g

Where:

m Mass of the particle g Acceleration due to gravity

Plugging in the values:

Fg 0.001 kg middot; 9.8 m/s2 0.0098 N

Electric Force Balance

The electric force Fe acting on a charge q in an electric field E is given by:

Fe q middot; E

Where:

q Charge of the particle E Electric field strength

Setting Forces Equal

Fe Fg

This gives us:

q middot; E m middot; g

Substituting the known values:

q middot; 160 N/C 0.0098 N

Solving for Charge

Rearranging the equation to solve for q:

q frac{0.0098 N}{160 N/C} 0.00006125 C

Determining the Sign of the Charge

Since the electric field is directed downward and we want the particle to remain stationary, the electric force must be upward. Therefore, the charge must be negative to counteract the gravitational force:

q -0.00006125 C or -61.25 μC

Conclusion

The charge of the particle must be:

-0.00006125 C or -61.25 μC

Final Calculation Summary

Given:

Electric field E 160 N/C Mass m 1g 10^-3 kg Acceleration due to gravity g 9.8 m/s^2

Substituting the values:

q -frac{m middot; g}{E} -frac{10^-3 kg middot; 9.8 m/s^2}{160 N/C} -6.125 middot; 10^-5 C

This value aligns with our earlier calculation, confirming the correctness of the charge and magnitude required for the particle to remain stationary in the electric field.