To determine the strength of the electric field [tex]\( E \)[/tex] of a point charge, we use the formula:
[tex]\[ E = \frac{k \cdot q}{r^2} \][/tex]
Given the information:
- The magnitude of the charge, [tex]\( q = 6.4 \times 10^{-19} \)[/tex] C
- The distance from the charge, [tex]\( r = 4.0 \times 10^{-3} \)[/tex] m
- Coulomb's constant, [tex]\( k = 9.00 \times 10^0 \)[/tex] [tex]\( \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]
Now, we proceed with the calculation step-by-step.
1. Substitute the given values into the formula:
[tex]\[ E = \frac{(9.00 \times 10^0) \cdot (6.4 \times 10^{-19})}{(4.0 \times 10^{-3})^2} \][/tex]
2. Square the distance:
[tex]\[ (4.0 \times 10^{-3})^2 = 16.0 \times 10^{-6} \][/tex]
3. Multiply the constants:
[tex]\[ 9.00 \times 6.4 = 57.6 \][/tex]
4. Substitute these intermediate results back into the formula:
[tex]\[ E = \frac{57.6 \times 10^{-19}}{16.0 \times 10^{-6}} \][/tex]
5. Simplify the fraction:
[tex]\[ E = \frac{57.6}{16.0} \times \frac{10^{-19}}{10^{-6}} = 3.6 \times 10^{-13} \][/tex]
Therefore, the strength of the electric field is:
[tex]\[ E = 3.6 \times 10^{-13} \text{ N/C} \][/tex]
Note that this does not match any of the given options directly, but rather, it appears that there may be a discrepancy. Let's reconsider if there is possibly a mistake in the options themselves. If we had to choose the closest option to our result, none of the provided answers match [tex]\( 3.6 \times 10^{-13} \)[/tex]. Therefore, it's possible there's an error in the provided options.
