How much work must be done to bring three electrons from a great distance apart to 1.0 * 10^(-10)m from one another (at the corners of an equilateral triangle)?
Get it by calculating the potential energy of the configuration.
It takes ke^2/a to bring the second charge within a of the first one, and 2ke^2/a to bring in the third one within a of both of the first two. That makes a total P.E. of
3 ke^2/a, and that is the work required.
k is the Coulomb constant and e is the electron charge.
V=k*q/r
so for the above equation, there should without square!
1.4*10^-17
To calculate the work required to bring three electrons from a great distance apart to a distance of 1.0 * 10^(-10) m from each other, we need to consider the electrostatic potential energy.
The electrostatic potential energy between two charged particles is given by the formula:
U = k * (q1 * q2) / r
where U is the potential energy, k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
In this case, since all three electrons have the same charge (let's assume -e for each electron, where e is the elementary charge), we can rewrite the formula as:
U = k * (q^2) / r
where q is the charge of a single electron.
To find the total work done to bring the electrons from a great distance apart to the given configuration, we need to sum up the potential energy of each pair of electrons. Since we have three electrons, there will be three pairs. The potential energy for each pair is the same, as each electron has the same charge.
Therefore, the total work done can be calculated as:
Work = 3 * U
Let's substitute the values into the equation:
Work = 3 * (k * (q^2) / r)
Now, we can plug in the values:
k = 8.99 * 10^9 Nm^2/C^2
q = -1.6 * 10^(-19) C (the charge of an electron)
r = 1.0 * 10^(-10) m
Work = 3 * (8.99 * 10^9 Nm^2/C^2 * (-1.6 * 10^(-19) C)^2 / (1.0 * 10^(-10) m))
Simplifying this expression will give us the final answer for the amount of work required to bring three electrons from a great distance apart to 1.0 * 10^(-10) m from one another.