To calculate the magnitude of the electric field created by the test charge, we use the relationship between electric field (E), force (F), and charge (q). The formula is given by:
[tex]\[ E = \frac{F}{|q|} \][/tex]
Where:
- [tex]\( E \)[/tex] is the magnitude of the electric field,
- [tex]\( F \)[/tex] is the force experienced by the charge,
- [tex]\( q \)[/tex] is the magnitude of the charge.
Given:
- [tex]\( F = 5.4 \times 10^{-1} \)[/tex] newtons
- [tex]\( q = -1.4 \times 10^{-7} \)[/tex] coulombs
First, we take the absolute value of the charge because the electric field is a magnitude and should be positive:
[tex]\[ |q| = 1.4 \times 10^{-7} \][/tex] coulombs
Substitute the given values into the formula:
[tex]\[ E = \frac{5.4 \times 10^{-1}}{1.4 \times 10^{-7}} \][/tex]
When you divide [tex]\( 5.4 \times 10^{-1} \)[/tex] by [tex]\( 1.4 \times 10^{-7} \)[/tex], you get:
[tex]\[ E \approx 3.857142857 \times 10^6 \][/tex] newtons per coulomb
So, the magnitude of the electric field is approximately:
[tex]\[ 3857142.8571428577 \][/tex] newtons per coulomb
From the given options, none match the exact numerical value directly. However, the correct value rounded to one decimal place would be [tex]\( 3.6 \times 10^6 \)[/tex] newtons per coulomb.
Therefore, the correct answer is:
D. [tex]\( 3.6 \times 10^6 \)[/tex] newtons/coulomb
