As illustrated in the figure, a convex lens of focal length 12 ext cm is situated within a uniform magnetic field B of magnitude 1.2 ext T oriented parallel to its principal axis. A particle with a mass of 2.0 imes 10⁻⁵ ext kg and a charge of 2.0 imes 10⁻³ ext C is projected perpendicular to the plane of the diagram at a speed of 4.8 ext m s ⁻¹ . The particle travels along a circular path whose centre lies on the pri

Step-by-step solution

The radius of the circular path of the charged particle in the magnetic field is given by: R = mv qB Substituting the given values: R = 2.0 10⁻⁵ 4.8 2.0 10⁻³ 1.2 = 9.6 10⁻⁵ 2.4 10⁻³ = 4 10⁻² m = 4 cm The circular path of the particle acts as an object for the convex lens. The plane of this circle is perpendicular to the principal axis. Given the object distance u = -18 cm and the focal length of the convex lens f = +12 cm . Using the lens formula: 1 v - 1 u = 1 f 1 v - 1 -18 = 1 12 1 v + 1 18 = 1 12 1 v = 1 12 - 1