A laboratory ion accelerator is designed to bring singly ionized xenon atoms (charge…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A laboratory ion accelerator is designed to bring singly ionized xenon atoms (charge magnitude e, mass mXe) to a final speed vf using two successive accelerating gaps. The first gap has a potential difference ΔV1 and the second gap has ΔV2. The ions start from rest and experience no forces other than those produced by the applied electric fields.
(a) Derive an expression for the total potential difference ΔVtot=ΔV1+ΔV2 that is required for the ions to reach the target speed vf.
(b) In terms of vf, determine the speed v1 of an ion immediately after it passes through the first gap if the two gaps have equal potential differences (ΔV1=ΔV2).
(c) Suppose the accelerator is redesigned so that ions leave the first gap with exactly half the final speed (v1=21vf). Show that the ratio of the potential differences must satisfy ΔV2ΔV1=31.
(d) Discuss one practical advantage and one practical disadvantage of using unequal potential differences in a multi-stage accelerator.