91Ó°ÊÓ

Charge motion is an essential concept in physics, especially when dealing with electric fields and charged particles. In this exercise, we focus on how a charged particle moves due to its interaction with an electric field.

A charged particle experiences a force when it is placed in an electric field. This is due to the interaction between the charge and the field, following the equation:

• Electric force: \( F = qE \)

where \( q \) is the charge, and \( E \) is the strength of the electric field. This force will influence how the particle moves in the field.

In this scenario, we have a small object with a charge of \(+9.00 \mu \mathrm{C}\) traveling in an electric field of \(895 \mathrm{~N/C}\) directed along the \( +y \) axis. This creates a force on the particle acting in the \( +y \) direction. Since gravitational effects are neglected here, only the electric force dictates the charge's motion in the \(y\)-direction.

Kinematics deals with the motion of objects without considering the forces causing the motion. Here, it is applied to describe the trajectory of our charged particle under the influence of an electric field.

One of the crucial elements in kinematics is determining positions under constant acceleration. The particle initially only has a velocity in the \(-x\)-direction at \(125 \mathrm{~m/s}\), and no initial velocity in the \(y\)-direction. Thanks to the electric force calculated earlier, acceleration in the \(y\)-direction can be determined using:

• Acceleration: \( a_y = \frac{F}{m} \)

and is utilized in the kinematic equation:

• Position: \( y = v_{y0}t + \frac{1}{2}a_yt^2 \)

Since the initial \(y\)-velocity \(v_{y0} = 0\), we focus on the change in position due to acceleration. By this logic, this approach helps compute the final displacement in the \(y\)-direction at a specific time \( t = 7 \mathrm{~ms}\).

In the \(x\)-direction, as there are no forces acting, the velocity remains constant. Thus, position in the \(x\)-direction is simply:

• \( x = v_xt \)

Newton's Second Law is fundamental when understanding the relationship between force and the motion it causes. The law states:

• \( F = ma \)

Where \( F \) is the force applied to an object, \( m \) is the mass of the object, and \( a \) is the acceleration it experiences.

In our scenario, the particle's acceleration in the \(y\)-direction is determined by this principle. With a known mass and a force calculated from the electric field and the charge, the acceleration is computed. This value tells us how quickly the object's velocity changes in the \(y\)-direction.

Knowing the acceleration allows us to apply kinematic equations and predict the future motion and final position of the charge accurately, when the effect of gravitational force is considered negligible. Newton's Second Law thus bridges the link between the force from the electric field and the resultant motion of a charged particle.