91Ó°ÊÓ

Newton's Second Law of Motion is one of the foundational principles of physics. It establishes the relationship between the motion of an object and the forces acting on it. According to this law, the force (\( F \)) acting on an object is equal to the mass (\( m \)) of that object multiplied by its acceleration (\( a \)). In mathematical terms, this is expressed as:\[ F = ma \]This equation tells us that a stronger force will result in a greater acceleration if the mass remains constant. Additionally, for the same mass, an increase in acceleration demands a greater force. Newton's Second Law connects to the concept of an electric field because when a charged object is placed in an electric field, the electric force acting upon the object causes it to accelerate. By using this principle, we can relate the electric force (\( F = qE \)) to Newton's formula (\( F = ma \)) and solve for the electric field (\( E \)). It serves as a bridge to understanding the dynamics of charged objects in electric fields.

Acceleration is a physical concept that describes how the velocity of an object changes over time. When an object speeds up, slows down, or changes direction, it is accelerating. In this particular exercise, the object experiences an acceleration given as (\( 2.5 \times 10^3 \text{ m/s}^2 \)). This acceleration is crucial as it helps us determine the force acting on the mass of the object, and thus the strength of the electric field.- Acceleration is a vector quantity, meaning it has both a magnitude (how much) and a direction (which way).- The unit of acceleration is meters per second squared (\( \text{m/s}^2 \)).Knowing the acceleration of the object, we can use Newton’s Second Law to find the force causing this acceleration. This force, in an electric context, is due to the electric field acting on the charge.

Charge is a fundamental property of matter that causes it to experience a force in an electric field. Electric charge comes in two types: positive and negative. In this exercise, the object has a charge of \(-34 \mu C \), which is equal to \(-34 \times 10^{-6} \text{ C}\). This negative charge plays a critical role in determining the direction of the electric force and the electric field itself.- Charges exert forces on each other: like charges repel, unlike charges attract.- The magnitude of the charge is the numerical value representing how much charge an object has.In an electric field, a charged object experiences a force (\( F = qE \)), which results in acceleration (\( F = ma \)). The sign of the charge affects the direction of the force. In our scenario, since the charge is negative, the electric field direction will be opposite to the acceleration direction.

The concepts of magnitude and direction are essential when discussing vectors in physics. The magnitude refers to the size or length of the vector, while the direction indicates where the vector points. For an electric field, the magnitude describes the strength of the field, and direction shows the path along which a positive charge would naturally move.In this problem:- The calculated magnitude of the electric field is \( 2.206 \times 10^5 \text{ N/C} \). This quantifies how strong the electric field is in influencing the charged object.- The direction is determined by the acceleration and charge. Given that the acceleration is in the \(+x\) direction, and the charge is negative, the electric field's direction is opposite to the acceleration, in the \(-x\) direction.Understanding magnitude and direction helps us not only calculate the force that causes the motion but also predict how the object will behave within the field.