Two electrons are fixed 2cm apart. Another electron is shot from infinity and comes to rest midway between the two fixed electrons.

A)Find the energy of the system initially( unknown quantity leave as a variable)
B) Find the final energy of the system?( unknown quantity leave as a variable)
C find the initial speed of the electron

To find the energy of the system initially, we can use the principle of conservation of energy. The total energy of the system is the sum of the potential energy and the kinetic energy.

A) We can represent the initial energy of the system as E_initial.

The potential energy of the system is given by the formula:

Potential Energy = (k * q1 * q2) / r,

where k is the electrostatic constant (9 × 10^9 Nm²/C²), q1 and q2 are the charges of the electrons, and r is the distance between them.

Since the distance between the fixed electrons is 2 cm, or 0.02 m, and the charge of each electron is 1.6 × 10^-19 C, the potential energy between the fixed electrons is:

Potential Energy = (9 × 10^9 Nm²/C²) * (1.6 × 10^-19 C)² / 0.02 m.

The kinetic energy of the electron at infinity is zero since it is at rest. Therefore, the initial energy of the system can be represented as:

E_initial = Potential Energy.

B) To find the final energy of the system, we need to consider the conservation of energy. The initial energy of the system will be converted into the final energy of the system. In this case, the final energy of the system will be potential energy between the two fixed electrons.

E_final = Potential Energy.

C) To find the initial speed of the electron, we can use the principle of conservation of mechanical energy. The initial energy of the system is equal to the final energy of the system. Therefore,

E_initial = E_final.

Since the initial kinetic energy of the electron is zero, the initial energy of the system is equal to the potential energy of the system. From part A, we have:

E_initial = (9 × 10^9 Nm²/C²) * (1.6 × 10^-19 C)² / 0.02 m.

Equating this to the final energy of the system, we can solve for the unknown variable, which represents the initial speed of the electron.