Work done by moving electrons through electric potential?

[nghpham]

Homework Statement

A parallel-plate capacitor is charged to an electric potential of 100 V by moving 4x10^19 electrons from one plate to the other. How much work was done?

Homework Equations

How much work was done?

The Attempt at a Solution

Work is then simply equals to -q*deltaV. Q= number of electrons times charge per electron.

W= +4E19 * 1.6E-19 * 100= 640 J

But the answer I was given was 320 J. I don't see a divisible of 2 anywhere that I can account for.

Please help. Thanks.

 

[cepheid]

Welcome to PF!

Homework Statement

A parallel-plate capacitor is charged to an electric potential of 100 V by moving 4x10^19 electrons from one plate to the other. How much work was done?

Homework Equations

How much work was done?

The Attempt at a Solution

Work is then simply equals to -q*deltaV. Q= number of electrons times charge per electron.

W= +4E19 * 1.6E-19 * 100= 640 J

But the answer I was given was 320 J. I don't see a divisible of 2 anywhere that I can account for.

Please help. Thanks.

The conceptual error you're making here is that V is not constant during the movement of the charges. In other words, the 100 V was not always there from the beginning, but rather it built up slowly from 0 V as the charge accumulated. So W = q*V won't work. Instead you need W = ∫qdV = ∫CVdV.

If you haven't done integrals before, then use the following (totally equivalent) method: look up the equation for the total energy stored in a capacitor.

 

[nghpham]

I see the error. Thank you much.

 

[truesearch]

The voltage built up from zero to 100V by transferring the charge. For a capacitor Q is proportional to V so to calculate the work done you need average voltage (V/2) x charge

 

[Nickie]

I would like to clarify that the work done in this scenario is indeed 640 J, as calculated in the attempt at a solution. The answer of 320 J may have been a mistake or miscalculation. It is important to double check calculations and units to ensure accuracy in scientific work. Additionally, it is important to note that the work done in this scenario is due to the movement of electrons through an electric potential, which is a fundamental concept in electromagnetism. This work is necessary to charge the parallel-plate capacitor to a potential of 100 V, and it can be calculated using the equation W = qΔV, where q is the charge and ΔV is the change in potential.