PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
An alpha particle (charge +2e, mass mα=6.64×10−27kg) is accelerated from rest through three collinear spherical conducting shells whose surfaces are maintained at the following electric potentials relative to infinity:
• Shell S₁: +500V
• Shell S₂: +200V
• Shell S₃: −100V
The alpha particle starts just outside S₁, passes through holes in each shell, and exits just outside S₃. Neglect gravitational forces.
(a) Express symbolically, in terms of e and the given potentials, the total electric potential difference experienced by the alpha particle from its starting position to its exit just outside S₃.
(b) Derive an expression for the particle’s speed as it leaves S₃, in terms of e, mα, and the potentials.
(c) Compute the numerical value of that speed.
(d) Briefly explain whether relativistic corrections are necessary for the speed obtained.