An electron is accelerated from rest through 2310V and then enters a region where there is a uniform 1.59-T magnetic field. What is the maximum force on the electron? Answer in units of Newtons.
To find the maximum force on the electron in the given scenario, we can use the following formula:
F = q * (E + v * B)
Where:
F: force on the electron
q: charge of the electron
E: electric field
v: velocity of the electron
B: magnetic field
First, let's calculate the charge of an electron (q). The charge of an electron is -1.6 x 10^-19 Coulombs.
Next, let's determine the electric field (E). The electric potential difference (V) given is 2310V. The electric field is the potential difference divided by distance (d). However, in this case, the distance is not provided. So, we need to use another approach.
Since the electron is accelerated, we know it gains kinetic energy given by the formula:
KE = qV
Where:
KE: kinetic energy
q: charge of the electron
V: potential difference
Substituting the known values:
KE = (-1.6 x 10^-19 C) * (2310V)
Now, we know that the kinetic energy of an electron is given by:
KE = 1/2 * m * v^2
Where:
m: mass of the electron
v: velocity of the electron
Taking the square root of both sides and rearranging the equation, we get:
v = sqrt((2 * KE) / m)
The mass of an electron (m) is 9.1 x 10^-31 kg.
Substituting the known values:
v = sqrt( (2 * (-1.6 x 10^-19 C) * (2310V)) / (9.1 x 10^-31 kg) )
Now that we have the velocity of the electron (v), we can calculate the force (F) using the given magnetic field (B):
F = q * (E + v * B)
Substituting the known values:
F = (-1.6 x 10^-19 C) * (0 + sqrt( (2 * (-1.6 x 10^-19 C) * (2310V)) / (9.1 x 10^-31 kg) ) * (1.59 T))
Calculating this expression will give us the maximum force on the electron in units of Newtons.