- #1
Jzhang27143
- 38
- 1
I am confused about the signs in calculating the potential energy change from the electrostatic force.
Suppose there was a point charge +q1 and I moved a second point charge +q2 from a distance of b from q1 to a distance of c from q1. c is smaller than b.
So the potential energy change is - ∫ F ⋅ ds where F is the electric force due to q1. F is radially outward and ds is dr radially inward (from b to c)$, so F⋅ds = - F dr. So - ∫ F⋅ds = ∫ F dr = ∫ Kq1q2 / r^2 dr from b to c so the integral is Kq1q2 (-1/c + 1/b) which is negative. But the potential energy should be positive when q2 is brought closer to q1. Where is the sign error?
Suppose there was a point charge +q1 and I moved a second point charge +q2 from a distance of b from q1 to a distance of c from q1. c is smaller than b.
So the potential energy change is - ∫ F ⋅ ds where F is the electric force due to q1. F is radially outward and ds is dr radially inward (from b to c)$, so F⋅ds = - F dr. So - ∫ F⋅ds = ∫ F dr = ∫ Kq1q2 / r^2 dr from b to c so the integral is Kq1q2 (-1/c + 1/b) which is negative. But the potential energy should be positive when q2 is brought closer to q1. Where is the sign error?