To determine the magnitude of the electric field at a point [tex]\(0.0055 \, \text{m}\)[/tex] from a [tex]\(0.0025 \, \text{C}\)[/tex] charge, we use Coulomb's law for the electric field, given by the formula:
[tex]\[ E = \frac{k q}{r^2} \][/tex]
where:
- [tex]\( E \)[/tex] is the electric field,
- [tex]\( k \)[/tex] is the electrostatic constant ([tex]\(9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)[/tex]),
- [tex]\( q \)[/tex] is the charge ([tex]\(0.0025 \, \text{C}\)[/tex]),
- [tex]\( r \)[/tex] is the distance from the charge ([tex]\(0.0055 \, \text{m}\)[/tex]).
Following these steps, we:
1. Substitute the value of [tex]\( k \)[/tex] into the equation:
[tex]\[ k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \][/tex]
2. Substitute the value of [tex]\( q \)[/tex] into the equation:
[tex]\[ q = 0.0025 \, \text{C} \][/tex]
3. Substitute the value of [tex]\( r \)[/tex] into the equation:
[tex]\[ r = 0.0055 \, \text{m} \][/tex]
4. Compute the square of [tex]\( r \)[/tex]:
[tex]\[ r^2 = (0.0055 \, \text{m})^2 = 3.025 \times 10^{-5} \, \text{m}^2 \][/tex]
5. Insert these values into the formula:
[tex]\[ E = \frac{(9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2) \times (0.0025 \, \text{C})}{(3.025 \times 10^{-5} \, \text{m}^2)} \][/tex]
6. Calculate the numerator:
[tex]\[ 9.00 \times 10^9 \times 0.0025 = 2.25 \times 10^{7} \][/tex]
7. Calculate the electric field [tex]\( E \)[/tex]:
[tex]\[ E = \frac{2.25 \times 10^7}{3.025 \times 10^{-5}} \approx 743801652892.562 \, \text{N/C} \][/tex]
The magnitude of the electric field is approximately:
[tex]\[ 7.4 \times 10^{11} \, \text{N/C} \][/tex]
Therefore, the correct answer is:
A. [tex]\( 7.4 \times 10^{11} \, \text{N/C} \)[/tex]
