A charged cloud system produces an electric field in the air...

A charged cloud system produces an electric field in the air near Earth's surface. A particle of charge $-2.0 \times 10^{-9} \mathrm{C}$ is acted on by a downward electrostatic force of $6.0 \times 10^{-6} \mathrm{~N}$ when placed in this field. (a) What is the magnitude of the electric field? What are the (b) magnitude and (c) direction of the electrostatic force $\vec{F}_{e l}$ on a proton placed in this field? (d) What is the magnitude of the gravitational force $\vec{F}_{g}$ on the proton? (e) What is the ratio $F_{e l} / F_{g}$ in this case? (f) If the proton is released, what is the magnitude of its acceleration?

Key Concepts

Electric Field

The electric field is a vector field that represents the force per unit charge that a charged particle would experience at any point in space. It is defined by the relation E = F/q, where F is the force experienced by a test charge q placed in the field. This concept allows the characterization of electric effects independent of the source charge that creates the field.

Electrostatic Force

The electrostatic force is the force that a charged particle experiences when placed in an electric field. It is given by the equation F = qE, where q is the charge of the particle and E is the electric field. This principle underlies how charged particles interact with electric fields, resulting in motion or other physical effects based on the magnitude and direction of the force.

Charge and Sign Convention

The concept of electric charge includes both magnitude and sign, and the sign determines the direction of the force in an electric field. When applying F = qE, a positive charge experiences a force in the direction of the electric field, while a negative charge experiences a force in the opposite direction. Understanding charge sign is essential for correctly determining the direction of forces in electrostatic problems.

Gravitational Force

Gravitational force is the attractive force exerted by a mass due to gravity. Near the surface of the Earth, it is given by F = mg, where m is the mass of the object and g is the acceleration due to gravity. This concept is important for comparing the influence of gravity with other forces, such as the electrostatic force in problems involving charged particles.

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, represented as F = ma. This fundamental law of motion is used to relate forces to the resulting acceleration of objects, and it is crucial for analyzing motion under the influence of multiple forces such as gravitational and electrostatic forces.

Force Ratio

The force ratio involves comparing the magnitudes of different forces acting on a particle—for example, the electrostatic force relative to the gravitational force. This concept is useful for understanding which force dominates in a given situation and for predicting the resulting behavior of the particle when released or subjected to these forces.

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