How much work is required to completely separate two charges (each -1.9 microC ) and leave them at rest if they were initially 6.0mm apart?

see other post.

To calculate the work required to separate two charges, we need to determine the change in potential energy as the charges are moved.

The potential energy between two charges is given by the formula:

U = k * (q1 * q2) / r

Where:
- U is the potential energy.
- k is Coulomb's constant (8.99 x 10^9 N m^2/C^2).
- q1 and q2 are the charges (-1.9 microC in this case).
- r is the distance between the charges.

Initially, the charges are 6.0 mm apart, which we'll convert to meters:
r = 6.0 x 10^-3 m

The initial potential energy is calculated with the given formula. However, since the charges are initially at rest, their total kinetic energy is zero.

As the charges are separated, the potential energy will increase. The work done to separate the charges is equal to the change in potential energy:

Work = ΔU = U_final - U_initial

At infinity, the potential energy between the charges becomes zero, so U_final = 0.

Therefore, the work required to completely separate the charges is equal to the initial potential energy:

Work = U_initial = k * (q1 * q2) / r

Plugging in the values:
k = 8.99 x 10^9 N m^2/C^2
q1 = -1.9 x 10^-6 C
q2 = -1.9 x 10^-6 C
r = 6.0 x 10^-3 m

Work = (8.99 x 10^9 N m^2/C^2) * (-1.9 x 10^-6 C) * (-1.9 x 10^-6 C) / (6.0 x 10^-3 m)

Simplifying the expression and calculating the result will give us the amount of work required to completely separate the charges.