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Coulomb's law is fundamental in understanding the forces between charged particles. It states that the electric force

• between two point charges is directly proportional to the product of their charges
• and inversely proportional to the square of the distance between them.

The formula for Coulomb's law is:\[ F = \frac{k \times |q_1 \times q_2|}{r^2} \]Here, \( k \) is Coulomb’s constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.
This law helps in calculating the forces that charged particles exert on each other.When two charges are equal and opposite, like the electrons in this problem, the forces do not always result in motion as they cancel each other out. Instead, they contribute to the electric potential energy. The distance between charges plays a crucial role since the force decreases as distance increases.In the exercise, even though the forces cancel out at the midpoint, they add up to affect the electron shot from infinity by modifying its potential energy.

The concept of kinetic energy is central to solving this problem. Kinetic energy is the energy of motion, defined by the formula:\[ KE = \frac{1}{2} m v^2 \]where \( m \) is mass and \( v \) is velocity. When the electron is shot from infinity, it initially possesses kinetic energy that decreases as it converts into electric potential energy, explained by energy conservation.

• Initially, all its energy is kinetic when it's far away from the other electrons.
• As it travels closer, it loses kinetic energy since this energy is converted into potential energy.
• Finally, it stops at the midpoint, where all its energy is electric potential energy.

By equating the initial kinetic energy to the potential energy at the stopping point, we solve for its initial velocity. It demonstrates how energy changes from one form to another, which is a fundamental concept in physics.

In the realm of electrostatics, charge interactions are crucial for understanding how forces and energies manifest.

• Like charges repel each other, while unlike charges attract.
• The interaction strength is governed by Coulomb's law, as discussed earlier.

Electric fields, created by charges, influence other charges within the field. In the exercise, the two fixed electrons produce an electric field that affects the electron shot from infinity.

The electron's movement is a result of these interactions:

• The forces from the fixed electrons tend to cancel, but the potential energy due to their fields remains significant.
• This potential energy ultimately dictates the electron's behavior, halting its motion at the midpoint.

Understanding these interactions helps in visualizing how electrons move through fields, a key aspect in fields like electronics and electromagnetism.