Chapter 27, Problem 27.81CP

A particle with charge 2.15 μC and mass 3.20 × 10⁻¹¹ kg is initially traveling in the +y-direction with a speed ʋ₀ = 1.45 × I0⁵ m/s. It then enters a region containing a uniform magnetic field that is directed into, and perpendicular to the page in Fig. P27.81. The magnitude of the field is 0.420 T. The region extends a distance of 25.0 cm along the initial direction of travel; 75.0 cm from the point of entry into the magnetic field region is a wall. The length of the field-free region is thus 50.0 cm. When the charged particle enters the magnetic field, it follows a curved path whose radius of curvature is R. It then leaves the magnetic field after a time t₁ having been deflected a distance Δx₁. The particle then travels in the field-free region and strikes the wall after undergoing a total deflection Δx. (a) Determine the radius R of the curved part of the path, (b) Determine t₁, the time the particle spends in the magnetic field, (c) Determine Δx₁, the horizontal deflection at the point of exit from the field, (d) Determine Δx, the total horizontal deflection.

Figure P27.81