Moving Charges and Magnetism

In a vacuum chamber, a particle of charge 1 and mass 1 mg is projected with a velocity ( i+2 j) m s-1 from the XZ plane at time t=0 in an electric field of 1 i V m-1. At t=0.2 s, the electric field is switched off and a magnetic field of 6 j T is switched on. The acceleration due to gravity is -10 j m s-2. Correct option(s) is/are:

1. The vertical distance of the particle from the XZ plane at t=0.3 s is 15 cm.
2. The vertical distance of the particle from the XZ plane at t=0.4 s is 10 cm.
3. The radius of the trajectory of the particle for t>0.2 s is 20 cm.
4. The particle will be in the XZ plane at t=0.35 s.

A positive, singly ionized atom of mass number AM is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width w with magnetic field B0 = 0.1 k Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory. [Given: Mass of neutron/proton = (5/3) 10-27 kg, charge of the electron = 1.6 10-19 C.] [figure] Which of the following option(s) is(are) correct?

1. The value of x for H+ ion is 4 cm.
2. The value of x for an ion with AM = 144 is 48 cm.
3. For detecting ions with 1 AM 196, the minimum height (x1 - x0) of the detector is 55 cm.
4. The minimum width w of the region of the magnetic field for detecting ions with AM = 196 is 56 cm.