Question

looking for help on all three portions including the bonus questios.

A beam of protons are all traveling in the same direction, but have a range of velocities. This beam of protons enters a region of magnetic field that is confined to a rectangular region, as shown. The magnitude of this magnetic field is measured to be 2.5 mT. If the protons remain in the plane of the page, and deflect down, as shown, what is the direction of the magnetic field? Protons of what velocity will emerge from the magnetic field (the bottom edge of the rectangle) with velocity straight down, as shown? Bonus: in Problem 4, determine the minimum and maximum velocities for which protons emerge from the bottom edge of the rectangle

Answer 1

a) Since the proton has a positive charge and the bending of motion is clockwise hence the direction of the magnetic field will, be out of page direction so that the velocity vector cross product with magnetic flux density vector could be towards the right at each point.

b) Here the radius of the circular motion is 15 cm and the magnitude of magnetic field is 2.5 mT then the formula:

q B where rho is the radius , m is mass, v is velocity, q is charge, B is magnetic field. 0.15 = 1.67*10^-27*v/(1.6*10^-19*2.5*10^-3) v = (1.6*10^-19*2.5*10^-3)*0.15/(1.67*10^-27) = 35928.1437 m/s