Three charges are located at the corners of a rectangle as follows:
Charge A: lower left corner, -3.0 μC
Charge B: upper left corner, -6.1 μC
Charge C: upper right corner, +2.7 μC
The distance between A and B is 0.16 m and between B and C it is 0.25 m.
How much work must an external force acting on the particles (like, your hands) do in order to move the charges infinitely far from each other?
Simple.
The energy to do this will be equal to the PE the system has:
PE=k(Q1*Q2)/d12 +k(Q1Q3)/d13 +kQ2Q3/d23
And what is neat, you do this by moving only two charges, that puts all three infinitely apart.
1.49J
To find the work done to move the charges infinitely far from each other, we need to calculate the total electrical potential energy of the system initially and then calculate it again when the charges are infinitely far apart. The difference between the two will give us the work done.
The formula for the electrical potential energy between two charges is given by:
U = k * (q1 * q2) / r
where U is the electrical potential energy, k is the electrostatic constant (k = 9.0 × 10^9 N·m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's calculate the potential energy between the charges first.
The potential energy between charges A and B:
U_AB = k * (q_A * q_B) / r_AB
= (9.0 × 10^9 N·m^2/C^2) * (-3.0 μC) * (-6.1 μC) / 0.16 m
The potential energy between charges B and C:
U_BC = k * (q_B * q_C) / r_BC
= (9.0 × 10^9 N·m^2/C^2) * (-6.1 μC) * (2.7 μC) / 0.25 m
Now, let's calculate the work done to move the charges infinitely far apart. When the charges are infinitely far apart, they will have zero electrical potential energy.
The work done is given by:
W = U_AB + U_BC
So, calculate the work done by adding the potential energies:
W = U_AB + U_BC
Finally, plug in the values and calculate the work done.