1. The problem statement, all variables and given/known data A particle with charge q and mass m is tied by a (I assumed stiff) string of length L to a pivot point P, all of which lie on a horizontal plane. A uniform electric field E is placed over this system. If the initial position of the particle is at a point where the string is displaced T degrees from the axis parallel to the electric field, what will be the speed of the particle when it reaches this axis? The particle is initially at rest. Assume no outside work is done on the particle. We are given E in V/m, q (the charge of the particle) in C, T in degrees, L in m, and mass in kg. 2. Relevant equations Energy(final) = Energy(initial) In a uniform E, potential difference = -E*displacement K (kinetic energy) = 1/2 mv^2 for v <<<< c (v way way less than c, so neglect the change in mass) U = qV 3. The attempt at a solution It seems a pretty simple problem up to the point I'm stuck at. I set up the general energy equation: K(initial) + U(initial) = K(final) + U(final) K(initial) = 0 (it starts at rest) K(final) = (mv^2)/2 and contains the final v I want Moving U(final) to the left side yields: U(initial)-U(final), or qV(initial) - qV(final), or q[V(initial)-V(final)], or q(deltaV) From this, we can see that by solving for v, we can easily find it. But wait! What's the potential difference (deltaV)? Easy - the work done to move the particle from its initial position to the final position, or just -E * displacement for a uniform electric field. Where I'm stuck: how should I go about measuring the displacement? I know I could solve a line integral, but I honestly think there's an easy answer to this, and I feel like I've done it before, but I just can't remember it. Help? Edit: Looking at this a little more, I thought of trying the ratio of the angles and the arcs. So, can I use: (T/360) = (displacement/circumference)?