Oh, that makes sense now. So setting the limits from a larger to smaller distance by itself establishes that the electric force is in the opposite direction of the displacement, meaning that the negative from the dot product is redundant.
Wait i thought the direction of ds was the direction of the path taken. Thats why I thought ds and the electric field pointed in opposite direction so the dot product was negative. If that's not the case, what determines the direction of ds?
well, I know that if an external agent is doing positive work, then the potential energy change is positive, and the potential energy change is negative if the external agent is doing negative work. In my example of moving q2 closer to q1, the work from the external agent should be positive and...
i'm not sure what the problem is with the integration. ∫ Kq1q2/r^2 dr from b to c is kq1 q2 ∫ dr/r^2 from b to c = kq1q2 (-1/r) from b to c = kq1q2(-1/c - (-1/b)) = kq1q2(-1/c + 1/b). Should i have done the integral from c to b? if so, why?
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 - ∫...
I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The...
Homework Statement
Given a semi-infinite stick (that is, one that goes off to infinity in one direction), determine how its density should depend on position so that it has the following property: If the stick is cut at an arbitrary location, the remaining semi-infinite piece will balance on a...
Ok I see that the direction should be flipped since theta is negative. That would give me T(theta) >= T(0) e^(u*theta). So is this the lower bound for T(theta) and the solution's T(theta) is the upper bound?
Homework Statement
A disk of mass M and radius R is help up by a massless string. Let there now be friction between the disk and the string, with coefficient u. What is the smallest possible tension in the string at its lowest point?
The problem is problem 8 from here...
You prepare 0.5 liters of a solution by adding 0.75 moles of a weak acid HA to water. For HA, Ka = 10^-1 Finally you dilute this solution to a final volume of 2.0 liters. What is the pH of the diluted solution?
My solution is this. [HA] = .75 mol /.5 L = 1.5 M. HA + H2O -> H3O+ + A-. If x...
OH. That makes so much sense. If R2 has E voltage and the emf is E, there can initially be no current from the emf. But as the capacitor discharges, the current from the emf increases so the circuit eventually reaches a "uniform" current.