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Imagine an electric field as an invisible force field that permeates space where charged particles are present. It is a vector quantity, which means it has both direction and magnitude, typically measured in newtons per coulomb (N/C). When a charge is placed in an electric field, it experiences a force in the direction of the field if the charge is positive, and opposite to the field if the charge is negative.

For example, in the exercise, the electric field is characterized by the vector \( \textbf{E}=(7800 \textbf{i}-4900 \hat{\textbf{j}}) \frac{N}{C} \) which specifies the field's magnitude and direction in a two-dimensional space. The positive and negative components represent the field's influence along the x and y axes of a coordinate system. In essence, this electric field would exert force on any charge placed within it, the magnitude and direction of which can be calculated using the formula \( F = q\textbf{E} \) where \( F \) is the force, and \( q \) is the charge of the particle.

Torque is a measure of the force that can cause an object to rotate around an axis. For an electric dipole鈥攁n entity consisting of two equal but opposite charges separated by distance鈥攑laced in an electric field, the torque is experienced as a twisting effect trying to align the dipole with the electric field lines.

The formula to compute the torque acting on a dipole is \( \tau = pE \sin \theta \) where \( \tau \) is the torque, \( p \) is the dipole moment, \( E \) is the electric field strength, and \( \theta \) is the angle between the dipole moment and the electric field vector. In the provided exercise, the dipole moment needs to be represented in component form to accurately calculate the torque since \( \theta \) is not explicitly given.

Electric potential energy (U) is the energy stored in a system of charged particles due to their positions in an electric field. For an electric dipole, this energy is dependent on the orientation of the dipole relative to the electric field. The formula \( U = -pE \cos \theta \) is used, where \( U \) is the potential energy, \( p \) is the dipole moment, \( E \) is the magnitude of the electric field, and \( \theta \) is the angle between the dipole moment and the electric field vector.

In our exercise scenario, the electric potential energy of the dipole in the given orientation to the electric field is calculated by determining the value of \( \cos \theta \) through the component form of \( p \) and \( E \) vectors. This represents the stored energy due to the particular configuration of the dipole in the field which would change if the dipole's orientation changes.

The coordinate system is a fundamental concept in physics that provides a framework for describing the position of points in space. In two dimensions, it typically consists of two perpendicular axes: x (horizontal) and y (vertical). By defining the position of an object with coordinates along these axes, its location can be clearly and mathematically described.

In the given problem, the coordinates of the positive and negative charges of the dipole are used to calculate the distance between them, which is crucial in finding the dipole moment. Understanding the coordinate system is also essential when calculating the components of vectors, such as the electric field and the dipole moment, which are necessary for computing torque and electric potential energy in this context.