Calculate the amount of work required to assemble a system of charges.

• ditde
In summary, the conversation discusses the calculation of the amount of work required to assemble a system of three charges at the corners of an isosceles triangle. The charges, Q1, Q2, and Q3, have values of 22.6*10^-6C, 22.6*10^-6C, and 61.0*10^-6C respectively. The sides of the triangle are given as a=4m and b=2m, with Q3 being 2m from Q1 and Q2, and Q1 being 4m from Q2. The problem assumes that the charges are brought in from infinity, with an initial voltage (Vi) of 0. The equation used
ditde

Homework Statement

The three charges shown below (Q1=22.6*10^-6C, Q2=22.6*10^-6C, Q3=61.0*10^-6C) are at the corners of an iscoceles triangle with sides a=4 m and b=2 m.

Q3 is 2m from Q1 and Q2, Q1 is 4m from Q2. In other words, Q3 is the point charge at the "tip" of the isosceles triangle.

Calculate the amount of work required to assemble this system of charges, assuming they are brought in from infinity.

Homework Equations

W = ΔPE = qΔV = q(Vi-Vf)
V = kQ/r

Being brought in from infinity means that Vi (initial voltage) = 0.

The Attempt at a Solution

I calculated the work required to bring in each charge individually and attempted to add them in the end.

Example of my working;

Work1 = Q1 * (0 - Vf)

Vf = kQ2/r2 + kQ3/r3

Work1 = 22.6*10^-6 * (0-(((9.10^9*22.6*10^-6)/4)+((9.10^9*61.0*10^-6)/2))

ditde said:
I calculated the work required to bring in each charge individually and attempted to add them in the end.
That is fine.
Try to work with units please, it is easier to find errors that way.

1. How do you calculate the amount of work required to assemble a system of charges?

The amount of work required to assemble a system of charges can be calculated by taking the sum of the work done to bring each individual charge from infinity to its final position, while keeping all other charges fixed.

2. What is the unit of measurement for work in this calculation?

The unit of measurement for work in this calculation is joules (J).

3. Is there a formula for calculating the work required to assemble a system of charges?

Yes, the formula for calculating the work required to assemble a system of charges is W = ∑(QiVi), where W is the total work, Qi is the charge of each individual charge, and Vi is the potential at the final position of each charge.

4. Can the work required to assemble a system of charges ever be negative?

Yes, the work required to assemble a system of charges can be negative if the charges are of opposite sign and are brought closer together, thus reducing the potential energy of the system.

5. How is the work required to assemble a system of charges related to the total potential energy of the system?

The work required to assemble a system of charges is directly related to the total potential energy of the system. This means that the higher the work required, the higher the potential energy of the system will be.

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