You’re working on a way of transporting alpha particles from where they are made to another room where they will collide with other material to form the isotopes. Since the radioactive isotopes are not expected to live very long, it is important to know precisely how much time it will take to transport the alpha particles. Your job is to design that part of the transport system, which will deflect the beam of alpha particles (m6.64 x 10-27 kg, q 3.2 x 10-19 C, Velocity 800000 m/s) through an angle of 90deg by using a magnetic field. The beam will be traveling horizontally in an evacuated tube. At the place the tube is to make a 90deg turn you decide to put a dipole magnet, which provides a uniform vertical magnetic field of 0.030 T. Your design has a tube of the appropriate shape between the poles of the magnet. Before you submit your design for consideration, you must determine how long the alpha particles will spend in the uniform magnetic field in order to make the 90deg-turn.
Note: the magnetic field is always perpendicular to the alpha particle. Lorentz force B * q * v 0.03 * 3.2 x 10E-19 * 800000 7.68 x E -15 This force causes the alpha particle to move in a circular path. The radius of the circle is given by equating the centripetal force of the circular motion to the Lorentz force. 7.68 * E -15 mv^2 / R Hence R 6.64 * E -27 * 800000^2 / (7.68 * E -15) 0.5533 m The particle must travel through a quarter circle to turn 90 deg. x 2 * pi * R / 4 3.14159 * 0.5533 / 2 0.869 m time spent to turn 90 deg x / v 0.869 / 800000 1.086 x E -6 sec or approx 1 micro sec.
