What Is the Relation Between Coulomb’s Law and The Electric Field?
By exerting pressures on one other, electric charge attract and repel each other. This force is described by Coulomb’s law. It is the fundamental law of electric charge interaction. Coulomb’s law is concerned with point charges in particular. Protons, electrons, and other fundamental components of matter can be used as point charges. Furthermore, any items can be considered as point charges as long as the distance between them is sufficiently short. Coulomb’s law states that the amount of the electric force between two-point charges is proportional to their magnitude and inversely proportional to their distance. Coulomb’s law is stated as follows for an electric force of size F:
The charge of point charge 1 is q1 in this formula, while the charge of point charge 2 is q2. The r between these point charges is the distance between them. The proportionality is defined by the Coulomb constant k, which will be described in detail further below. The force’s direction is a vector that runs along the line that connects the two charges. According to Newton’s Third Law, the forces on the two-point charges create an action-reaction pair. This indicates that the amount of the force is the same on both point charges, and the forces are in opposing directions. The forces are repulsive and directed away from the other charged item if the two charges have the same sign (both positive or both negative). If the two charges have opposing signs, the forces are attracted to each other and point in the direction of the other charged item. Whether the force is attractive or repulsive determines the sign of the vector force. The unit vector can be used to represent a direction that follows the charge line. The vector force can be expressed as follows:
The Coulomb is the unit of electric charge in SI units. It is one of the SI system’s basic units. The letter C is used to symbolise the Coulomb unit. The charge values q1 and q2 are given in Coulombs in the following formula, with either a positive or negative sign. The value of r in SI units is represented in metres (m), and the result is a force F in Newtons (N). The value of the constant k in Coulomb’s law was found experimentally to be:
The permittivity of free space is a constant that may be expressed in terms of the constant k. The Greek letter (“epsilon”) with a subscript zero is used as the symbol for this constant. “Epsilon-nought” is how it’s pronounced. The worth of is,
As a result, Coulomb’s law is frequently written:
The formula in both variants is the same. Only multiples of the electron or proton charge can be subdivided in charge. Any charge value must be a multiple of this number. The charge magnitude with the lowest feasible magnitude is denoted by the letter e. Object charges are frequently expressed as multiples of e for clarity. A combination of 10 protons and 8 electrons, for example, would have a charge of:
Superposition of Forces
The forces that act between two-point charges are defined by Coulomb’s law. When more point charges are added to the equation, the forces on each charge add up. This is referred to as force superposition. The total force on a point charge is equal to the vector sum of the forces exerted by the other charges when two or more charges individually exert a force on it.
An electric field is emitted by every charged item. This electric field is the source of the electric force experienced by other charged particles. A charge’s electric field exists everywhere, although its intensity diminishes with distance squared. The electric field unit in SI is Newtons per Coulomb, or N/C. A test charge can be used to determine the electric field of a charged item. A test charge is a tiny charge that may be used to map an electric field at various locations. The test charge is designated as q0. An electric field exists at a given location if a test charge is placed there and feels an electrostatic force. Fo denotes the electrostatic force at the test charge’s location. The electric field, like electrostatic force, is a vector quantity. The electrostatic force at a given location is equal to the test charge q0 divided by the electric field at that location:
This formula may be adjusted to solve for the electrostatic force on the test charge q0 if the electric field at a certain location is known:
The connection between the electric field and electrostatic force directions is determined by the sign of the test charge. The force and field vectors have the same direction if the test charge is positive. The force and field vectors have the opposite directions if the test charge is negative.
How to solve: Five point charges, each of value +q coul, are placed on five vertices of a regular hexagon of isde L meters. The magnitude of the force on the point charge of value -q coul, placed at the centre of the hexagen is?
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