To find the strength of the electric field of a point charge, we use the formula:
[tex]\[ E = \frac{k \cdot q}{r^2} \][/tex]
where:
- [tex]\( E \)[/tex] is the electric field strength,
- [tex]\( k \)[/tex] is Coulomb's constant,
- [tex]\( q \)[/tex] is the magnitude of the point charge,
- [tex]\( r \)[/tex] is the distance from the charge.
Given values:
- [tex]\( k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex],
- [tex]\( q = 6.4 \times 10^{-19} \, \text{C} \)[/tex],
- [tex]\( r = 4.0 \times 10^{-3} \, \text{m} \)[/tex].
First, we calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (4.0 \times 10^{-3} \, \text{m})^2 \][/tex]
[tex]\[ r^2 = 16.0 \times 10^{-6} \, \text{m}^2 \][/tex]
Next, we calculate the electric field strength [tex]\( E \)[/tex] by substituting the given values into the formula:
[tex]\[ E = \frac{9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \times 6.4 \times 10^{-19} \, \text{C}}{16.0 \times 10^{-6} \, \text{m}^2} \][/tex]
We calculate the numerator:
[tex]\[ 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \times 6.4 \times 10^{-19} \, \text{C} = 57.6 \times 10^{-10} \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
Now, we divide the numerator by the denominator:
[tex]\[ E = \frac{57.6 \times 10^{-10} \, \text{N} \cdot \text{m}^2 / \text{C}}{16.0 \times 10^{-6} \, \text{m}^2} \][/tex]
Simplifying the division:
[tex]\[ E = \frac{57.6 \times 10^{-10}}{16.0 \times 10^{-6}} \][/tex]
[tex]\[ E = 3.6 \times 10^{-4} \, \text{N} / \text{C} \][/tex]
Thus, the electric field strength is:
[tex]\[ 3.6 \times 10^{-4} \, \text{N} / \text{C} \][/tex]
So, the correct answer is:
[tex]\[ \text{D. } 3.6 \times 10^{-4} \, \text{N} / \text{C} \][/tex]
