To determine the magnitude of the electric force on an electron in an electric field, we use the formula:
[tex]\[ F = |q \cdot E| \][/tex]
where:
- [tex]\( F \)[/tex] is the magnitude of the electric force,
- [tex]\( q \)[/tex] is the charge of the electron, and
- [tex]\( E \)[/tex] is the strength of the electric field.
Given values are:
- The charge of the electron ([tex]\( q \)[/tex]) is [tex]\( -1.6 \times 10^{-19} \)[/tex] coulombs.
- The electric field ([tex]\( E \)[/tex]) is [tex]\( 1.4 \times 10^5 \)[/tex] newtons/coulomb.
First, we consider the magnitude of the charge and ignore the sign because we need the magnitude of the force:
[tex]\[ q = 1.6 \times 10^{-19} \text{ coulombs} \][/tex]
Next, we multiply the charge by the electric field to find the force:
[tex]\[ F = (1.6 \times 10^{-19} \text{ coulombs}) \times (1.4 \times 10^5 \text{ newtons/coulomb}) \][/tex]
This multiplication gives:
[tex]\[ F = 2.24 \times 10^{-14} \text{ newtons} \][/tex]
Thus, the magnitude of the electric force on the electron due to the electric field is:
[tex]\[ 2.24 \times 10^{-14} \text{ newtons} \][/tex]
The correct answer is:
C. [tex]\( 2.2 \times 10^{-14} \text{ newtons} \)[/tex]
