Work needed to move a point charge

In summary, the problem involves calculating the work required to move a +0.50μC test charge from a point midway between two +30μC charges to a point 10cm closer to one of the charges. The relevant equations are W = qV and V = kQ/r. The attempt at a solution involved using +30μC as the Q value, r as 0.32m, and q as the test charge, but the answer received was incorrect. The correct answer is 1.08 Joules, and the work done is equal to the change in potential energy between the two locations. However, it is unclear how to calculate this given that both charges are pushing the test charge away.
  • #1
TrpnBils
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Homework Statement



A +30μC charge is placed 32cm from an identical charge. How much work would be required to move a +0.50μC test charge from a point midway between them to a point 10cm closer to one of the charges.

Homework Equations


W = qV
V = kQ/r


The Attempt at a Solution



Tried solving with +30μC as the Q value, r as 0.32m, and q as the test charge but I'm getting this wrong. The answer is 1.08 Joules. I know that the work done = ΔPE between the two locations, but I'm not sure how to calculate this given that BOTH charges on the ends are pushing it away...
 
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  • #2
TrpnBils said:

Homework Statement



A +30μC charge is placed 32cm from an identical charge. How much work would be required to move a +0.50μC test charge from a point midway between them to a point 10cm closer to one of the charges.

Homework Equations


W = qV
V = kQ/r

The Attempt at a Solution



Tried solving with +30μC as the Q value, r as 0.32m, and q as the test charge but I'm getting this wrong. The answer is 1.08 Joules. I know that the work done = ΔPE between the two locations, but I'm not sure how to calculate this given that BOTH charges on the ends are pushing it away...
What is the electric potential, due to the two +30μC charges, at a point midway between them and at a point 10cm closer to one of the charges.
 

1. What is the definition of "work" in terms of moving a point charge?

The work needed to move a point charge is the amount of energy required to move the charge from one point to another against an external force. It is measured in joules (J).

2. How is the work needed to move a point charge calculated?

The work needed to move a point charge is calculated by multiplying the magnitude of the charge (q) by the potential difference (V) between the two points (W = qV). This equation is based on the fact that work is equal to the force applied multiplied by the distance moved in the direction of the force.

3. What is the relationship between work and the direction of the electric field?

The direction of the electric field determines the direction of the force on a point charge. The work needed to move the point charge is positive if it moves in the same direction as the electric field and negative if it moves in the opposite direction. This is because work is defined as the product of the force and the displacement in the direction of the force.

4. Can the work needed to move a point charge be negative?

Yes, the work needed to move a point charge can be negative. This occurs when the point charge moves in the opposite direction of the electric field. In this case, the force and displacement are in opposite directions, resulting in a negative value for work.

5. How does the distance between two points affect the work needed to move a point charge?

The work needed to move a point charge is directly proportional to the distance between the two points. This means that the farther apart the points are, the more work is needed to move the charge between them. This relationship is based on the inverse-square law, where the strength of the electric field decreases as the distance between two points increases.

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