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In the world of electricity, the point charge stands out as a fundamental concept. A point charge is a charged particle with a very small size compared to the distances we are examining. This concept simplifies the calculations because the charge can be considered as concentrated at a single point in space. When using the term 'point charge', it often implies that this charge affects its surroundings entirely based on its magnitude and distance from other objects.
The charge is often denoted by the symbol \( Q \), and its magnitude is measured in Coulombs (\( ext{C} \)). In the given exercise, the point charge is \(-3.0 \times 10^{-5} \ ext{C}\) and is located at the origin of the coordinate system. This negative value of the charge will have implications on the direction of the electric field it creates.

Coulomb's constant, represented by the symbol \( k \), plays a key role in electrostatics, especially in calculating electric fields and forces between charges. It provides the proportionality necessary to relate the electric forces to the charges involved and their separation distance. The accepted value of this constant in a vacuum is \( 8.99 \times 10^9 \ ext{N}\cdot\text{m}^2/\text{C}^2 \).
This constant is derived from Coulomb’s law, which states that the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. In our exercise, \( k \) is used in the formula to calculate the electric field produced by a point charge. It factors into how strongly the electric field interacts with surrounding points in space.

The electric field formula is incredibly useful for determining the strength of the field generated by a point charge at any position in space. The formula is:

• \( E = \frac{k \cdot |Q|}{r^2} \)

This equation suggests that the electric field \( E \) depends on several factors:

• The absolute value of the charge \( Q \), which dictates the magnitude of the field.
• The inverse square of the distance \( r \) from the charge. This means that as you get farther from the charge, the field gets weaker quite rapidly.

This formula allows us to predict not just the strength but also consider the potential direction of the field when calculating effects due to the charge. Since the charge in the given exercise is negative, although the magnitude is used in calculations, the field direction itself is influenced by the charge's negativity.

The coordinate system is crucial for determining positions in physical space relating to the point charge. It provides a framework where one can locate the position of the charge and the point where the electric field is being calculated. Generally, this is done in a simple Cartesian coordinate system with an \( x \)-axis, \( y \)-axis, and sometimes \( z \)-axis, but often only one is necessary for simpler problems.
In the current exercise, the point charge is at the origin, which is \((0,0)\) in this system, while the electric field is being calculated at point \((5.0 \ ext{m}, 0)\), meaning the point lies along the positive direction of the \( x \)-axis. Setting up the coordinate system this way simplifies many calculations and visually aids in understanding the problem.

A negative charge, like the one given in the exercise, influences the direction of the electric field it creates. While positive charges emit electric fields that point outward from the charge, negative charges attract electric field lines inward towards themselves.
In the specific exercise, the charge placed at the origin is \(-3.0 \times 10^{-5} \ ext{C} \). Such a negative sign indicates that any electric field generated will point towards the origin from wherever it's calculated in space. Even though the magnitude of the field was calculated using the absolute value of the charge, the direction is indeed towards the charged particle due to its negative nature. Understanding this can be crucial for predicting the motion of other charged particles in proximity or interpreting the results of more complex electric field scenarios.