To find the force acting on the electrons moving in a magnetic field, we can use the formula for the magnetic force on a charged particle moving in a magnetic field:
[tex]\[ F = q \cdot v \cdot B \][/tex]
where:
- [tex]\( F \)[/tex] is the force acting 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 magnetic field strength [tex]\( B = 4.5 \times 10^{-2} \text{ T} \)[/tex],
- The velocity of the electrons [tex]\( v = 6.5 \times 10^6 \text{ m/s} \)[/tex],
- The charge of the electron [tex]\( q = -1.6 \times 10^{-19} \text{ C} \)[/tex].
Using the formula:
[tex]\[ F = q \cdot v \cdot B \][/tex]
Substitute the given values into the equation:
[tex]\[ F = (-1.6 \times 10^{-19} \text{ C}) \cdot (6.5 \times 10^6 \text{ m/s}) \cdot (4.5 \times 10^{-2} \text{ T}) \][/tex]
Calculate the product of the numbers (keeping track of the exponents):
[tex]\[ F = (-1.6) \cdot (6.5) \cdot (4.5) \times 10^{-19 + 6 - 2} \][/tex]
[tex]\[ F = -46.8 \times 10^{-15} \][/tex]
Simplify the exponent:
[tex]\[ F = -4.68 \times 10^{-14} \text{ N} \][/tex]
Therefore, the force acting on the electrons is:
[tex]\[ F = -4.68 \times 10^{-14} \text{ N} \][/tex]
The correct answer among the given choices is:
C. [tex]\(-4.9 \times 10^{-14} \text{ N}\)[/tex]
