Understanding Electric and Magnetic Fields: Forces and Charges

**Coulomb's Law: Quantifying Force Between Electric Charges**

The quantification of force between electric charges is attributed to Coulomb, who used a torsion balance. Coulomb's law states that the force of attraction or repulsion between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed as:

F = K • (Q₁Q₂ / r²)

Where:

• F is the force
• K is Coulomb's constant
• Q₁ and Q₂ are the charges
• r is the distance between the charges

The electrical constant, K, is defined in terms of another constant called the permittivity of the medium. Coulomb's law is analogous to Newton's law of universal gravitation. Both forces are proportional to the product of the property that creates them (mass or charge) and inversely proportional to the square of the distance between them. Both are central forces, but there are significant differences. Gravitational forces are always attractive, while electrical forces can be repulsive. G, the universal gravitational constant, is independent of the environment, while K depends on the medium in which the charges are located.

**Concept of Electric Field**

An electric field exists in a region of space if an electric charge introduced into this region experiences a force. The electric field intensity is defined as the force per unit of electric charge:

E = F / q = K • (Q / r²) • u_r

Where:

• E is the electric field strength
• F is the force
• q is the test charge
• K is Coulomb's constant
• Q is the source charge
• r is the distance from the source charge
• u_r is the unit vector in the direction of r

The electric field strength in the International System of Units (SI) is measured in Newtons per Coulomb (N/C).

**Electric Force and Potential Energy**

Electric force is a central and conservative force. Therefore, a scalar function called electric potential energy can be defined at each point:

U = K • (Q₁Q₂ / r)

The work done between two points, A and B, equals the negative change of U between those two points. The potential energy at a point can be defined as the work performed by the electric force to move a charge from that point to infinity, considering the potential energy at infinity to be zero.

**Concept of Electric Charge**

Electric charge is a property of matter, similar to mass. There are two types of charges in nature, arbitrarily named negative (-) and positive (+). Electric charge is a scalar magnitude measured in Coulombs (C) in the SI. Millicoulombs (mC) and microcoulombs (µC) are also commonly used. Two electrically charged bodies exert forces of attraction or repulsion on each other. If the charges have the same sign, the force is repulsive; if they have different signs, it is attractive.

Matter is composed of atoms, which in turn are made up of protons, electrons, and neutrons. Protons are positively charged, and electrons are negatively charged. The magnitude of the charge of both particles is the same. An atom is neutral when it has an equal number of protons and electrons. Protons are strongly bound in the nucleus, while electrons are weakly bound in the outer shell, making it relatively easy to separate them from the atom with a sufficient energy input.

**Charge States**

1. A body has a positive (+) charge when it has a deficiency of electrons.
2. A body has a negative (-) charge when it has an excess of electrons.

**Magnetic Field**

A magnet or a moving charge creates a magnetic field in the surrounding space. This field is characterized by the vector B, called magnetic induction. To characterize magnetic induction, we will analyze its effects on a point charge.

When an electric charge is placed in a region of space where a magnetic field exists, the following observations are made:

1. If the charge is at rest, no force acts upon it.
2. If the charge is in motion:
   1. There is a direction of velocity at which no force acts on the charge.
   2. When the velocity is perpendicular to the direction mentioned above, the force on the charge is maximum.
   3. The force is perpendicular to the velocity, and its magnitude is proportional to the velocity.
   4. The force is proportional to the charge and changes direction when the sign of the charge changes.

The mathematical relationship is given by the formula:

F = q • (v x B)

Where:

• F is the magnetic force
• q is the charge
• v is the velocity of the charge
• B is the magnetic induction

The force is perpendicular to the plane formed by the velocity and magnetic induction. The direction and sense of the force can be determined using the right-hand rule for the vector product.