A laboratory wants to separate the charged and neutral components of a decay beam…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A laboratory wants to separate the charged and neutral components of a β− decay beam consisting of 1MeV electrons and antineutrinos that emerge from a thin foil target. The particles enter a 50 m long evacuated tube that contains a uniform magnetic field B directed vertically upward and perpendicular to the initial particle velocity, which is horizontal.
(a) Derive an expression for the radius r of curvature of an electron moving at speed v in the magnetic field B.
(b) Explain why the antineutrinos travel essentially in straight lines through the same field.
(c) A detector is placed 50 m downstream and is designed to register only those particles that have been deflected horizontally by at least 0.50 m from the original beam axis. Using the non-relativistic approximation for the electron velocity, determine the minimum magnetic-field strength Bmin that will ensure all electrons are deflected enough to be detected, while all antineutrinos miss the detector.
(d) Identify and discuss two practical challenges that would still limit the laboratory’s ability to detect the antineutrinos with this apparatus, even after the charged particles have been removed.