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.
The potential energy of the electron at infinity is zero because it is very far away from the other two fixed electrons. When the electron stops midway between the two fixed electrons, the potential energy is also zero since the distance between the three electrons is at its minimum.
Initially, the electron will have kinetic energy due to its initial speed. At the midway point, all of the initial kinetic energy will have been converted to potential energy.
The potential energy between the electron and the fixed electrons can be calculated using Coulomb's law:
Electric potential energy (U) = (k * Q1 * Q2) / r
Where:
k = Coulomb's constant (8.99 × 10^9 N m^2/C^2)
Q1 = charge of the first electron
Q2 = charge of the second electron
r = distance between the two fixed electrons
Since the electrons have the same charge, Q1 = Q2 = e (electron charge) = 1.6 × 10^-19 C.
Given that the distance between the fixed electrons is 2 cm (0.02 m) and the potential energy is zero at the midway point, we can set up the equation:
0 = (k * e^2) / r
Rearranging the equation to solve for the initial speed (v):
v = sqrt((2 * k * e^2) / r)
Plugging in the values:
v = sqrt((2 * 8.99 × 10^9 N m^2/C^2 * (1.6 × 10^-19 C)^2) / 0.02 m)
Calculating the equation will give us the initial speed of the electron shot from infinity.