Two stationary positive point charges, charge 1 of magnitude 3.90 nC and charge 2 of magnitude 1.80 nC, are separated by a distance of 46.0 cm. An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

What is the speed vfinal of the electron when it is 10.0 cm from charge 1?

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Explanation:

When the electron moves, the gain in its kinetic energy is equal to the decrease in its electric potential energy, since the total energy must be conserved.

Therefore, we can write:

where

is the final kinetic energy of the electron, where

is its mass

v is its final speed

is the initial kinetic energy (the electron starts from rest)

is the initial electric potential energy, where

k is the Coulomb's constant

is the charge 1

is the electron charge

is the initial distance of the electron from charge 1

is charge 2

is the initial distance of the electron from  charge 2

is the final electric potential energy, where

is the final distance between electron and charge 1

is the final distance between electron and charge 2

Substituting everything we find:

So the final kinetic energy is

And therefore, the final speed is:

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