Final answer:
To calculate the radius of the path an electron will follow when subjected to a perpendicular magnetic field after being accelerated through a voltage, we first find the electron's velocity with the given potential difference using the energy principle. Then, with the electron's velocity, we plug the values into the radius formula considering the charge and mass of an electron and the magnetic field strength.
Step-by-step explanation:
The question involves calculating the radius of the path an electron will follow, when it is accelerated from rest through a potential difference and thereafter enters a region with a magnetic field perpendicular to its velocity. This is a classic physics problem combining concepts of electromagnetism and kinematics.
To find the radius (r) of the path of an electron moving through a magnetic field, we can use the formula r = mv/eB where m is the mass of the electron, v is the velocity of the electron, e is the charge of the electron, and B is the magnetic field strength.
First, we determine the velocity of the electron after being accelerated through a potential difference (V) using the energy principle eV = (1/2)mv^2. Solving for v, we get v = sqrt(2eV/m). Plugging the given values, the known mass of an electron (9.11 × 10^-31 kg), and the charge of an electron (1.60 × 10^-19 C) into this equation, we can solve for v. Then, we can use the value of v to calculate the radius r using the earlier mentioned formula, substituting the given value of the magnetic field strength (B = 4 mT or 4 × 10^-3 T).