A beam of protons passes through a velocity selector consisting of crossed uniform electric and magnetic fields. The electric field is 5 10^4 ~V/m and the magnetic field is 0.1 ~T . The protons then enter an adjoining region containing only a transverse uniform magnetic field of 0.05 ~T . In this region, the protons trace a semicircular path and hit a detector plate. The distance from the entry slit to the point of i

Step-by-step solution

In the velocity selector, the protons move undeflected, which means the electric force and magnetic force are equal in magnitude: qE = qvB₁ v = E B₁ Substituting the given values for the selector region: v = 5 10^4 0.1 = 5 10^5 ~m/s When the protons enter the second region with magnetic field B₂ , they undergo uniform circular motion. The radius r of the semicircular path is: r = mv qB₂ Substituting the values: r = 1.6 10⁻²⁷ 5 10^5 1.6 10⁻¹⁹ 0.05 r = 5 10⁻²² 0.05 10⁻¹⁹ r = 5 10⁻²² 5 10⁻²¹ = 0.1 ~m Converting the ra