Final answer:
The final speed of the electron is found using the principle of conservation of energy, where the initial potential energy at the midpoint between the charges is converted into kinetic energy as the electron moves towards one of the charges.
Step-by-step explanation:
The problem involves finding the final speed of an electron as it moves in an electric field created by two stationary positive point charges. To solve this, we can apply the principle of conservation of energy. Since the electron starts from rest at the midpoint between the two charges, its initial potential energy is converted into kinetic energy as it moves closer to charge 1.
First, we calculate the initial potential energy, which is the sum of the potentials due to both charges at the midpoint:
U = k(e) * (q1/r1 + q2/r2)
Where k(e) is Coulomb's constant, q1 and q2 are the magnitudes of the two charges, and r1 and r2 are their respective distances from the midpoint.
Then, we find the potential energy when the electron is 10.0 cm from charge 1:
U' = k(e) * (q1/r1' + q2/r2')
The change in potential energy (ΔU) is:
ΔU = U' - U
The final kinetic energy (Kf) of the electron is equal to the change in potential energy, since the electron starts from rest.
Kf = ΔU = ½ mv^2
Finally, we solve for the final speed v:
v = √(2Kf/m)
Where m is the mass of the electron. Plugging in the values and solving for v gives the final speed of the electron.