A narrow, evacuated rail of length accelerates singly charged ions of mass from rest.…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A narrow, evacuated rail of length 0.30m accelerates singly charged ions of mass 2.2×10−26kg from rest. Along the rail the electric potential V(x) varies only with the horizontal position x (measured from the starting point) according to the data in the table.
Position x(m) : 0.00 | 0.10 | 0.20 | 0.30
Potential V(V) : 0 | +400 | +650 | +800
(a) Using the tabulated potentials, determine the ion’s speed at each of the three indicated positions (0.10 m, 0.20 m, and 0.30 m).
(b) Sketch a qualitative graph of the ion’s speed v versus position x from 0 m to 0.30 m. Clearly label key values on both axes.
(c) Explain how conservation of energy accounts for the shape of your graph in part (b), making explicit reference to electric potential energy and kinetic energy.
(d) Suppose an identical but doubly charged ion (charge +2e) were launched under the same conditions. Without further calculation, describe how the speed-versus-position graph would compare to that for the singly charged ion, and justify your reasoning.