- #1
Lost1ne
- 47
- 1
From my interpretation of this problem (image attached), the force applied to the point charge is equal and opposite to the repulsive Coulomb force that that point charge is experiencing due to the presence of the other point charge so that the point charge may be moved at a constant velocity. I agree that the equation should yield a positive value, and I agree that the equation is valid, but I'm still a bit confused.
I don't see why this equation would hold if I used this evaluation of the dot product: \vec F \cdot d \vec r = | \vec F | * | d \vec r | * cos(Θ). (My LaTeX failed, but I hope you can see what I mean.) Our applied force vector and charge displacement vector are in the same direction. With that being said, as cos(0) = 0, I wouldn't see why our integral would have the negative sign on the left of the equality. However, removing this negative sign would of course change our answer, resulting in a negative value which would be an incorrect answer. Why does this approach with this interpretation of the dot product not seem to work (or, more likely, where does my thinking go wrong)?
I don't see why this equation would hold if I used this evaluation of the dot product: \vec F \cdot d \vec r = | \vec F | * | d \vec r | * cos(Θ). (My LaTeX failed, but I hope you can see what I mean.) Our applied force vector and charge displacement vector are in the same direction. With that being said, as cos(0) = 0, I wouldn't see why our integral would have the negative sign on the left of the equality. However, removing this negative sign would of course change our answer, resulting in a negative value which would be an incorrect answer. Why does this approach with this interpretation of the dot product not seem to work (or, more likely, where does my thinking go wrong)?
Attachments
Last edited: