Certainly! Let's break this down step by step.
1. Identify the known quantities:
- The charge [tex]\(q\)[/tex] is [tex]\(9.0 \times 10^{-5}\)[/tex] Coulombs.
- The electric field strength [tex]\(E\)[/tex] is [tex]\(4.0 \times 10^4\)[/tex] Newtons per Coulomb [tex]\( \left( \frac{N}{C} \right) \)[/tex].
2. Recall the formula for electrical force:
The electrical force [tex]\(F\)[/tex] on a charge [tex]\(q\)[/tex] in an electric field [tex]\(E\)[/tex] is given by:
[tex]\[
F = q \cdot E
\][/tex]
3. Substitute the known values into the formula:
[tex]\[
F = (9.0 \times 10^{-5} \, \text{C}) \cdot (4.0 \times 10^4 \, \frac{N}{C})
\][/tex]
4. Perform the multiplication:
[tex]\[
F = 9.0 \times 4.0 \times 10^{-5} \times 10^4 \, \text{N}
\][/tex]
Multiply the numeric coefficients:
[tex]\[
9.0 \times 4.0 = 36
\][/tex]
Handle the powers of ten:
[tex]\[
10^{-5} \times 10^4 = 10^{-5 + 4} = 10^{-1}
\][/tex]
5. Combine the results:
[tex]\[
F = 36 \times 10^{-1} \, \text{N}
\][/tex]
6. Express the final result:
[tex]\[
F = 3.6 \, \text{N}
\][/tex]
So, the electrical force acting on the charge is [tex]\(3.6\)[/tex] Newtons.
