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The electric force is a fundamental interaction between objects that possess an electric charge. According to Coulomb's law, the electric force (\( F_E \)) between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula is given by \( F_E = k \frac{|q_1 * q_2|}{r^2} \) where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

In our exercise, the electric force is considered acting on a single charge in an electric field, which can be derived from Coulomb's law and defined as \( F_E = qE \) where \( q \) is the charge of the particle, and \( E \) is the electric field strength. The direction of this force depends on the sign of the charge: it's in the direction of the field for a positive charge and opposite for a negative charge.

The gravitational force is another fundamental interaction and it's always an attraction between two masses. Unlike the electric force, which can attract or repel, gravity only pulls objects together. Newton's law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line joining both points. This force is proportional to the product of their masses and inversely proportional to the square of the distance between them. The equation for gravitational force (\( F_G \) is \( F_G = G \frac{m_1 * m_2}{r^2} \) where \( G \) is the gravitational constant.

When considering objects near the Earth's surface, the gravitational force can be simplified to \( F_G = mg \) where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity. The exercise uses this simplified formula, equating it to the electric force to find the balance for a stationary object in an electric field.

The charge of a particle is an intrinsic property that determines its electromagnetic interactions. Charges can be positive or negative, and like charges repel each other, while unlike charges attract. The unit of electric charge is the coulomb (\( C \) which is a relatively large unit; subatomic particles like protons and electrons carry a charge of approximately \( \pm1.6 \times 10^{-19} C \).

In the context of the given exercise, calculating the charge, \( q \), necessary for a particle to remain stationary in an electric field, involves balancing the electric force with the gravitational force. The sign of the charge (positive or negative) will determine the direction of the electric force exerted on the particle. For a negatively charged particle, the electric force is in the direction opposite to the gravitational force, which allows the particle to remain stationary when these two forces are equal.

Electrostatics is the study of electric charges at rest. It encompasses the behaviors of forces between charges that are not moving. Key concepts include electric charge, electric field, electric potential, and the behavior of conductors and insulators. An electric field (\( E \) is a vector field that represents the influence a charge exerts on other charges around it, and is defined as the force per unit charge. It is measured in newtons per coulomb (\( N/C \) or volts per meter (\( V/m \) and can be visualized with field lines emanating from positive charges and ending on negative charges.

The core principle we're applying in the exercise is that a stationary charged particle in an electric field is experiencing no net force, which means the electrostatic force is being exactly balanced by another force, in this case, gravity. Solving problems in electrostatics often involves understanding and manipulating the relationships between charge, electric field, and force.