Calculating Work Required to Move a Charge Between Two Identical Charges

  • Thread starter cashmoney805
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In summary: If you want the work done by an external force, use W = qΔV. So for this problem, W(by E) = -2.5J and Wext = 2.5J.In summary, the work required to move a +.5\muC test charge midway between two +35\muC charges to a point 12cm closer to either of the charges is +2.5J, as the charge is moving from an area of lower to higher potential. The formula used to calculate this work is W = qΔV, where Wext represents the work done by an external force and ΔV is the change in potential.
  • #1
cashmoney805
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Homework Statement


A +35[tex]\mu[/tex]C charge is placed 32 cm from an identicle +35[tex]\mu[/tex]C charge. How much work would be required to move a +.5[tex]\mu[/tex]C test charge midway between them to a point 12cm closer to either of the charges?


Homework Equations


Wext = -qV
V = kQ/r


The Attempt at a Solution


Q= +35[tex]\mu[/tex]C, q = +.5[tex]\mu[/tex]C
I found the initial V, Vi = 2KQ/.16 and then the final V, Vf = KQ[1/.28 +1/.04]
Then I did W = -q(Vf-Vi) and got -2.5J
However, the answer is +2.5 J. This makes sense that the answer is positive- you're moving a + charge from an area of lower to higher potential. Why doesn't this agree with my formula though?
 
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  • #2
cashmoney805 said:
Why doesn't this agree with my formula though?
Because you are finding the work done by you to move the charge, which is qΔV, not the work done by the field, which is -qΔV.
 
  • #3
Oh, so Wext = qΔV. So for energy considerations, is it W(by E) + PEi + KEi = PEf + KEf + Wext?
 
  • #4
cashmoney805 said:
Oh, so Wext = qΔV.
In this particular case, in which you are moving the charge with the least amount of energy (no excess kinetic energy).
So for energy considerations, is it W(by E) + PEi + KEi = PEf + KEf + Wext?
In general, I would say: PEi + KEi + Wext = PEf + KEf
 
  • #5
Ok. If another problem asks about W from E, would Wext just be negative in the equation you provided?
 
  • #6
If you want the work done by the electric field, use W = -qΔV.
 

1. What is work in relation to moving a charge?

Work is the transfer of energy that occurs when a force is applied over a certain distance. In the context of moving a charge, work is done when a force is applied to move the charge from one point to another.

2. Does the amount of charge affect the work required to move it?

Yes, the amount of charge does affect the work required to move it. The larger the charge, the more work is required to move it a certain distance. This is because the force needed to move a charge is directly proportional to the amount of charge.

3. How does the direction of the force affect the work required to move a charge?

The direction of the force does not affect the work required to move a charge. Work is a scalar quantity, meaning it only depends on the magnitude of the force and the distance moved, not the direction of the force.

4. Is the work required to move a charge always positive?

No, the work required to move a charge can be either positive or negative. Positive work is done when the force and displacement are in the same direction, while negative work is done when the force and displacement are in opposite directions.

5. How is electric potential energy related to work done in moving a charge?

Electric potential energy is the energy that a charge possesses due to its position in an electric field. The work done in moving a charge is equal to the change in electric potential energy. If the charge is moved against the direction of the electric field, work is done and the electric potential energy increases. If the charge is moved in the direction of the electric field, work is done and the electric potential energy decreases.

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