Two electrons are fiXed 2 cm apart .another eleCtron is shot from infinity and stops midway between the two .what is the initial speed?
To find the initial speed of the electron shot from infinity, we can use the principle of conservation of energy.
Initially, the electron is at infinity, meaning it has zero potential energy but possesses some initial kinetic energy. When the electron comes to a stop midway between the two fixed electrons, it has reached a potential energy value equal to the initial kinetic energy.
Let's assume the mass of the electron is "m" and its charge is "e". The distance between the fixed electrons is 2 cm (or 0.02 m). At the midpoint, the total potential energy of the electron is given by:
Potential Energy = Force * Distance
= (Electrostatic Force between electron and one fixed electron) * (distance from one fixed electron to the midpoint)
= (k * (e^2) / (distance from one fixed electron to the midpoint))
Here, k represents the Coulomb's constant (approximately equal to 9 x 10^9 Nm^2/C^2).
The initial kinetic energy of the electron can be equated to the potential energy:
Initial Kinetic Energy = Potential Energy
(1/2) m(v^2) = k (e^2) / d
where v is the initial speed of the electron and d is the distance from one fixed electron to the midpoint.
From the given scenario, we can determine that d = 0.01 m (half the distance between the two fixed electrons). Now, we can rearrange the equation to solve for the initial speed (v):
v = √((2 * k * (e^2) / (m * d)))
Substituting the known values, we can calculate the initial speed. The mass of an electron is approximately 9.1 x 10^-31 kg, and the charge of an electron is approximately 1.6 x 10^-19 C.