An electron is placed in a uniform electric field of strength 232 N / C. If the electron is at r

step 1 The x relation is given by A is equal to QE divided by M. Well, it is the magnitude of the elect

An electron is placed in a uniform electric field of...

An electron is placed in a uniform electric field of strength $232 \mathrm{N} / \mathrm{C}$. If the electron is at rest at the origin of a coordinate system at $t=0$ and the electric field is in the positive $x$ -direction, what are the $x$ - and $y$ -coordinates of the electron at $t=2.30 \mathrm{ns} ?$

Key Concepts

Component Analysis in Two-Dimensional Motion

In problems involving motion in two dimensions, the analysis is typically separated into independent components. Since the electric field affects only the component of motion in one direction (in this case, the x-direction), the motion in the perpendicular direction (the y-direction) remains unaffected and can often be treated as having zero acceleration.

Uniform Electric Field

A uniform electric field is one in which the electric field strength and direction are constant throughout the region. In such a field, any charged particle experiences a constant force, and if the particle starts from rest, it will experience a uniform acceleration in the direction dictated by its charge and the field direction.

Electric Force on Charges

The force acting on a charged particle within an electric field is given by the relation F = qE, where q is the charge of the particle and E is the electric field. This relation determines not only the magnitude of the force but also its direction, which is opposite for negative charges like electrons compared to positive charges.

Newton's Second Law

Newton's Second Law, F = ma, relates the net force experienced by an object to its acceleration and mass. For a charged particle in an electric field, after calculating the electric force using F = qE, one can determine the acceleration by dividing the force by the particle’s mass.

Kinematic Equations for Uniform Acceleration

When an object experiences constant acceleration, its displacement can be determined using the kinematic equations, such as x = x0 + v0t + 0.5at^2. This equation is particularly useful for calculating the position of a particle that starts from rest and moves under constant acceleration in a specific coordinate direction.

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