Let's break down the given problem and identify the correct solution by examining the options carefully.
The options provided for the electric potential energy of a charge positioned [tex]\(9.8 \times 10^{-5} m\)[/tex] from the source of the electric field are as follows:
1. [tex]\(3.5 \times 10^{-8} J\)[/tex]
2. [tex]\(4.6 \times 10^{-4} J\)[/tex]
3. [tex]\(2.7 \times 10^{-1} J\)[/tex]
4. [tex]\(3.7 J\)[/tex]
To determine the correct answer, let's carefully compare these numerical values:
1. [tex]\(3.5 \times 10^{-8} J\)[/tex]:
- This is a very small value, denoted in scientific notation [tex]\(10^{-8}\)[/tex], indicating that it is a small fraction, [tex]\(0.000000035 J\)[/tex].
2. [tex]\(4.6 \times 10^{-4} J\)[/tex]:
- This value is slightly larger, indicated by [tex]\(10^{-4}\)[/tex], which means [tex]\(0.00046 J\)[/tex].
3. [tex]\(2.7 \times 10^{-1} J\)[/tex]:
- This value is significantly larger compared to the previous ones, represented by [tex]\(10^{-1}\)[/tex] which translates to [tex]\(0.27 J\)[/tex].
4. [tex]\(3.7 J\)[/tex]:
- This is the largest value among the options, and it is expressed in a straightforward manner as [tex]\(3.7 J\)[/tex].
It's clear that comparing all options, the electric potential energy [tex]\(4.6 \times 10^{-4} J\)[/tex] seems to be the most plausible value given the context of the range and typical magnitudes of electric potential energy values.
Thus, the correct answer is:
[tex]\[ \boxed{4.6 \times 10^{-4} J} \][/tex]
