To find the magnitude of the electric force [tex]\( F \)[/tex] on an electron due to an electric field [tex]\( E \)[/tex], we use the equation:
[tex]\[ F = q \cdot E \][/tex]
where:
- [tex]\( q \)[/tex] is the charge of the electron, which is [tex]\( -1.6 \times 10^{-19} \)[/tex] coulombs
- [tex]\( E \)[/tex] is the electric field, which is [tex]\( 1.4 \times 10^{5} \)[/tex] newtons per coulomb
Since we are asked for the magnitude of the force, we'll use the absolute value of the charge:
[tex]\[ |q| = 1.6 \times 10^{-19} \][/tex] coulombs
Now, plug the values into the formula:
[tex]\[ F = (1.6 \times 10^{-19} \, \text{C}) \times (1.4 \times 10^{5} \, \text{N/C}) \][/tex]
Now, perform the multiplication of the numerical coefficients and add the exponents for the powers of ten:
[tex]\[ F = 1.6 \times 1.4 \times 10^{-19+5} \][/tex]
[tex]\[ F = 2.24 \times 10^{-14} \][/tex]
So, the magnitude of the electric force on the electron is:
[tex]\[ F = 2.24 \times 10^{-14} \][/tex] newtons
Comparing this result with the given options:
A. [tex]\( 1.6 \times 10^{-3} \)[/tex] newtons
B. [tex]\( 1.4 \times 10^{24} \)[/tex] newtons
C. [tex]\( 2.2 \times 10^{-14} \)[/tex] newtons
D. [tex]\( 7.4 \times 10^{-13} \)[/tex] newtons
E. [tex]\( 4.5 \times 10^{14} \)[/tex] newtons
The correct answer is:
C. [tex]\( 2.2 \times 10^{-14} \)[/tex] newtons
