A circular region of radius R=3 m has magnetic field -0.2k̂ T in the upper half and +0.2k̂ T in the lower half. A narrow beam of particles with m=2 g, v=0.3 m/s and q=+1 mC enters along a diameter. A screen is placed as shown. If the separation of impact points is 4X metres, find X.

Question

G1 Physics · Accepted Answer

The orbit radius in either half is r=mv/(qB)=(0.002×0.3)/(0.001×0.2)=3 m=R. The two beam portions therefore follow symmetric semicircular arcs to the screen, producing impact points 12 m apart. Since separation=4X, X=3.