Final answer:
To find the radius of the path for an electron that is accelerated by a voltage of 500 V and then subjected to a magnetic field of 100 mT, physics principles of electromagnetism and circular motion of charged particles are applied. After calculating the electron's kinetic energy and velocity, the radius can be determined using the ratio of the magnetic force to the centripetal force required for circular motion.
Step-by-step explanation:
The subject question involves determining the radius of the path that an electron will take when moving through a magnetic field after being accelerated by a known voltage. To find the radius of the path for an electron that is accelerated from rest by applying a voltage of 500 V and then subjected to a magnetic field of 100 mT, we use the principles of circular motion and the force exerted on a charged particle in a magnetic field.
The kinetic energy (KE) gained by the electron when accelerated by the potential difference (V) is equal to the work done on the electron by the electric field. The kinetic energy can be expressed as:
KE = eV
Where:
e is the charge of the electron (1.6×10−19 C), and
V is the potential difference (500 V)
We can then calculate the velocity (v) of the electron using the following relation:
KE = ½mv2
After finding the velocity, we can determine the radius (r) of the circular path in the magnetic field (B) using the following formula that comes from equating the centripetal force needed for circular motion to the magnetic force:
r = ½mv2 / (eB)
Upon calculating with the given values, we would find the correct radius matching one of the provided options (a through d). This exercise is a practical application of electromagnetism, a key concept in physics education.