what particles with electrical charges repel one another

Protons repel each other.

Electrons repel each other.

Particles with like electrical charges repel one another. This means that positively charged particles repel other positively charged particles, and negatively charged particles repel other negatively charged particles. To understand why this happens, let's explore the concept of electric charge.

Electric charge is a fundamental property of matter. It comes in two types: positive and negative. Protons, which carry a positive charge, and electrons, which carry a negative charge, are examples of elementary particles that possess electric charge.

According to Coulomb's Law, the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The mathematical expression for this force is F = k * (q1 * q2) / r^2, where F is the force between the particles, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the electrostatic constant.

When two particles have the same charge (both positive or both negative), their charges in the equation have the same sign. Since they are multiplied together, the product of two positive charges or two negative charges will always be positive. Thus, the force between them is positive as well, indicating a repulsive force. This repulsion is what causes particles with like electrical charges to instinctively move away from each other.

In summary, particles with the same electrical charge repel one another because of the nature of electric forces and Coulomb's Law. The repulsive force arises from the positive product of their charges, leading to an overall positive force that pushes the particles apart.