Change in potential energy/work formula for electric charges.

In summary, the formula ΔU = U_a - U_b = q(V_a - V_b) represents the change in potential energy from a to b. The work done by the electric field on a charge q when it moves from a to b is represented by W(ab)=Ua-Ub. The charge can be positive or negative, but the sign can be omitted when only the magnitude of work is of interest. Ohm's Law states that current is equal to the potential drop divided by resistance.
  • #1
theBEAST
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I have the following formula on my formula sheet:
ΔU = U_a - U_b = q(V_a - V_b)

I was wondering if 'a' is final and 'b' is initial or is it the other way around? Also when I plug in my charge q into the formula, if it was a negative charge do I plug the negative sign into the formula? I realize that some formulas assume that you plug in the magnitude of the charge so I am not so sure about this formula... Thanks!
 
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  • #2
The change of potential energy from a to b is Ub-Ua=q(Vb-Va), but the work done by the electric field on a charge q when it moves from a to b is W(ab)=Ua-Ub. If the charge moves in free space the work done by the field increases its kinetic energy: Ub-UA=KE(b)-KE(a), which means that U+KE=const, conservation of energy.


Imagine that the (positive) charge moves across a resistor from a to b. The moving charge constitutes current; the current flows from positive to negative, in the direction of decreasing potential: I=(Va-Vb)/R, and the work done (and dissipated on the resistor) while q charge moves from a to b is q(Va-Vb). Va-Vb sometimes is called "voltage" or "potential drop". Ohm's Law means that Current=potential drop divided by resistance.

The charge q can be either positive or negative, but you can omit the sign when you are interested only in the magnitude of work .


ehild
 

1. How do you calculate the change in potential energy for electric charges?

The change in potential energy for electric charges can be calculated using the formula ΔPE = qΔV, where ΔPE is the change in potential energy, q is the charge, and ΔV is the change in voltage.

2. What is the unit of measurement for electric potential energy?

The unit of measurement for electric potential energy is joules (J).

3. Can the work formula for electric charges be used for both positive and negative charges?

Yes, the work formula for electric charges can be used for both positive and negative charges. The only difference is that the work will be positive for positive charges and negative for negative charges.

4. How does the distance between charges affect the change in potential energy?

The change in potential energy is directly proportional to the distance between charges. As the distance increases, the change in potential energy decreases, and vice versa.

5. Can the work formula for electric charges be applied to systems with multiple charges?

Yes, the work formula for electric charges can be applied to systems with multiple charges. In this case, the change in potential energy will be the sum of the individual changes in potential energy for each charge.

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