Task id12030

A beam of positive singly charged ions (charge +e) of equal and constant mass m is emitted from point Q in one plane. Ions accelerated by voltage U are deflected by a uniform magnetic field, which is directed perpendicular to the plane of propagation of the ions. The magnetic field induction is equal to B. The boundaries of the magnetic field must be such that the ion beam converges at one point A (QA = 2a). The ion trajectories must be symmetrical relative to a line perpendicular to the segment QA and passing through its middle. From the possible boundaries of the magnetic field, one should choose those that would be in the vicinity of a line perpendicular to the middle of the segment QA, but would not include points Q and A. The region should be simply connected, i.e. no holes or tears. 1. Express the radius of curvature R of the particle trajectory in a magnetic field as a function of voltage V and induction B. 2. Indicate the characteristic properties of the particle trajectory in the described installation. 3. Find the boundaries of the magnetic field by geometric construction for the cases: Ra. 4. Find a mathematical expression for the magnetic field boundary.