Two electrons start at rest with a seperation of 5e-12 metres. Once released, the electrons accerelate away from each other. Calculate the speed of each electron when they are a very large distance apart.
To calculate the speed of each electron when they are a very large distance apart, we can consider the principle of conservation of energy.
The initial potential energy of the system is equal to the final kinetic energy when the two electrons are a very large distance apart. We can calculate the initial potential energy using Coulomb's law:
Potential energy (initial) = k * (q1 * q2) / r
where k is the electrostatic constant (k = 8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the electrons (q1 = q2 = -1.6 * 10^-19 C, since electrons have equal negative charges), and r is the separation distance between the electrons (r = 5 * 10^-12 m).
The final kinetic energy of each electron when they are far apart is given by:
Kinetic energy (final) = (1/2) * m * v^2
where m is the mass of each electron (m = 9.11 * 10^-31 kg), and v is the speed of each electron.
By equating the initial potential energy to the final kinetic energy, we have:
k * (q1 * q2) / r = (1/2) * m * v^2
Simplifying and solving for v, we get:
v = sqrt((2 * k * (q1 * q2) / r) / m)
Substituting the values, we have:
v = sqrt((2 * 8.99 * 10^9 Nm^2/C^2 * (-1.6 * 10^-19 C)^2) / (9.11 * 10^-31 kg * 5 * 10^-12 m))
Calculating the numerical value of v, we find:
v ≈ 2.19 * 10^6 m/s
Therefore, the speed of each electron when they are very far apart is approximately 2.19 * 10^6 m/s.
potential energy of each at start
= k q^2/r
at large distance that energy is kinetic so
(1/2)m v^2 = k q^2/r