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A charge of [tex]\( 9.0 \times 10^{-5} \, C \)[/tex] is placed in an electric field with a strength of [tex]\( 4.0 \times 10^4 \, \frac{N}{C} \)[/tex]. What is the electrical force acting on the charge?

[tex]\[ \square \, N \][/tex]

Sagot :

GinnyAnswer
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.
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