The maximum distance the beam penetrates into the region is equal to the radius of the circular path. Therefore, the maximum distance is 1.01 × 10^-3 meters.
The solution: Given:
A beam of electrons is initially moving along the negative x-axis.
The initial velocity of the electrons is 9.18 × 10^6 m/s.
The magnetic field in the region is 2.86 mT.
The magnetic field points in the positive y-direction.
Find:
The maximum distance the beam penetrates into the region.
Solution:
The magnetic field will cause the electrons to deflect in a circular path. The radius of this path is given by:
r = mv / (qB)
where:
m is the mass of an electron (9.11 × 10^-31 kg)
v is the velocity of the electrons
q is the charge of an electron (1.60 × 10^-19 C)
B is the magnetic field strength
Plugging in the values, we get:
r = (9.11 × 10^-31 kg)(9.18 × 10^6 m/s) / (1.60 × 10^-19 C)(2.86 × 10^-3 T)
r = 1.01 × 10^-3 m
The maximum distance the beam penetrates into the region is equal to the radius of the circular path.
Therefore, the maximum distance is 1.01 × 10^-3 meters.