To determine the force acting on the electrons, we can use the formula for the magnetic force on a charged particle moving perpendicular to a magnetic field, which is given by:
[tex]\[ F = qvB \][/tex]
Where:
- [tex]\( F \)[/tex] is the force on the electron.
- [tex]\( q \)[/tex] is the charge of the electron.
- [tex]\( v \)[/tex] is the velocity of the electron.
- [tex]\( B \)[/tex] is the magnetic field strength.
Given the values:
- [tex]\( B = 4.5 \times 10^{-2} \)[/tex] tesla
- [tex]\( v = 6.5 \times 10^5 \)[/tex] meters/second
- [tex]\( q = -1.6 \times 10^{-19} \)[/tex] coulombs
Substituting these values into the formula, we get:
[tex]\[ F = (-1.6 \times 10^{-19} \, \text{C}) \times (6.5 \times 10^5 \, \text{m/s}) \times (4.5 \times 10^{-2} \, \text{T}) \][/tex]
Multiplying these values:
[tex]\[ F = -1.6 \times 10^{-19} \times 6.5 \times 10^5 \times 4.5 \times 10^{-2} \][/tex]
[tex]\[ F = -4.68 \times 10^{-15} \, \text{N} \][/tex]
Therefore, the force acting on the electrons is:
[tex]\[ -4.68 \times 10^{-15} \, \text{N} \][/tex]
Now, we compare this result to the given options:
A. [tex]\( -29 \times 10^5 \, \text{N} \)[/tex] - This is not the correct answer.
B. [tex]\( -39 \times 10^{-14} \, \text{N} \)[/tex] - This is not the correct answer.
C. [tex]\( -4.5 \times 10^{-14} \, \pi \)[/tex] - This is not the correct answer.
D. [tex]\( -6.5 \times 10^{-13} \, \text{N} \)[/tex] - This is not the correct answer.
None of the provided options exactly matches our calculated answer, but the correct result is [tex]\(-4.68 \times 10^{-15} \, \text{N}\)[/tex]. This is close to the result we have calculated. So, please review the problem statement and the given options again for possible typo or miscalculation in the provided options.
