Final answer:
The radius of the circular path that electrons follow in a magnetic field is derived by equating the magnetic force to centripetal force, leading to the equation r = mv/(qB).
Step-by-step explanation:
To obtain the radius r of the circular path followed by an electron moving in a magnetic field, we start by equating the magnetic force to the centripetal force required to keep the electron moving in a circle.
The magnetic force FB acting on a charge q moving with velocity v at a right angle to a magnetic field B is given by FB = qvB. To maintain circular motion, this force must equal the centripetal force, which is given by Fc = mv2/r, where m is the mass of the electron.
Setting these two forces equal gives us qvB = mv2/r. When we solve this equation for the radius r, we get r = mv/(qB). This formula relates the radius r of the circular path to the mass m, charge q, velocity v, and magnetic field B.