To determine the magnitude of the electric field at the location where a particle with a charge [tex]\(+3.3 \times 10^{-18} \text{ C}\)[/tex] experiences a force of [tex]\(2.5 \times 10^{-8} \text{ N}\)[/tex], we can use the relationship between the electric field [tex]\(E\)[/tex], the force [tex]\(F\)[/tex], and the charge [tex]\(q\)[/tex]. This relationship is given by the formula:
[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 charge.
Given the values:
- [tex]\(F = 2.5 \times 10^{-8} \text{ N}\)[/tex]
- [tex]\(q = +3.3 \times 10^{-18} \text{ C}\)[/tex]
We can plug these values into the formula to find [tex]\(E\)[/tex]:
[tex]\[ E = \frac{2.5 \times 10^{-8}}{3.3 \times 10^{-18}} \][/tex]
By performing the division, we get:
[tex]\[ E \approx 7575757575.757575 \text{ N/C} \][/tex]
Thus, the magnitude of the electric field at this location is approximately [tex]\(7.6 \times 10^9 \text{ N/C}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{7.6 \times 10^9 \text{ N/C}} \][/tex]
