Proton in an electric field (a) What force (in dynes) acts...

Proton in an electric field (a) What force (in dynes) acts upon a proton in an electric field of 100 statvolts $/ \mathrm{cm} ?$ (b) If a proton were released at rest in a uniform field of this intensity, what would be its speed after $10^{-8} \mathrm{~s}$ ? (c) How far would it be from its release point after this time?

Proton in an electric field
(a) What force (in dynes) acts upon a proton in an electric field of 100 statvolts $/ \mathrm{cm} ?$
(b) If a proton were released at rest in a uniform field of this intensity, what would be its speed after $10^{-8} \mathrm{~s}$ ?
(c) How far would it be from its release point after this time?

Key Concepts

CGS Electrostatic Units

In the CGS (centimeter-gram-second) system, units such as statvolts for electric potential and dynes for force are used. This system defines electromagnetic quantities differently from the SI system and requires careful handling of unit conversions. Understanding these units is crucial when solving problems in electromagnetism that are presented within the CGS framework.

Electric Field

An electric field is a region in space where a charged particle experiences a force due to the presence of other charges. The electric field is a vector quantity and its magnitude and direction at any point dictate the force acting on a test charge placed there. This concept is central to understanding interactions between charges and the behavior of charged particles in various physical situations.

Force on a Charged Particle

The force experienced by a charged particle in an electric field is given by the equation F = qE, where F is the force, q is the charge of the particle, and E represents the electric field. This relationship shows that the electric force is directly proportional to both the magnitude of the charge and the strength of the electric field, and it acts in the direction of the field for positive charges.

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 (F = ma). In problems involving charged particles in an electric field, this law is used to relate the force due to the electric field to the resulting acceleration of the particle.

Kinematic Equations

When an object moves under constant acceleration, its velocity and displacement can be determined using kinematic equations. For instance, the equations v = at and d = 0.5at² (where v is velocity, a is acceleration, t is time, and d is displacement) are commonly used to calculate how fast the object moves and how far it travels over a given time period.

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