To find the electric potential energy (U) of a charge placed in an electric field, we use the formula:
[tex]\[ U = q \times E \times d \][/tex]
where:
- [tex]\( q \)[/tex] is the charge,
- [tex]\( E \)[/tex] is the electric field strength,
- [tex]\( d \)[/tex] is the distance from the source of the electric field.
Given the values:
- Charge ([tex]\( q \)[/tex]) = [tex]\( 4.5 \times 10^{-5} \)[/tex] C,
- Electric field strength ([tex]\( E \)[/tex]) = [tex]\( 2.0 \times 10^4 \)[/tex] [tex]\(\frac{N}{C}\)[/tex],
- Distance ([tex]\( d \)[/tex]) = 0.030 m.
We can substitute these values into the formula:
[tex]\[ U = (4.5 \times 10^{-5} \, \text{C}) \times (2.0 \times 10^4 \, \frac{\text{N}}{\text{C}}) \times (0.030 \, \text{m}) \][/tex]
Calculate the product step-by-step:
1. Multiply the charge by the electric field strength:
[tex]\[ 4.5 \times 10^{-5} \, \text{C} \times 2.0 \times 10^4 \, \frac{\text{N}}{\text{C}} = 9.0 \times 10^{-1} \, \text{N} \cdot \text{m} \][/tex]
2. Multiply the result by the distance:
[tex]\[ 9.0 \times 10^{-1} \, \text{N} \cdot \text{m} \times 0.030 \, \text{m} = 27.0 \times 10^{-3} \, \text{J} = 0.027 \, \text{J} \][/tex]
Therefore, the electric potential energy of the charge is [tex]\(\boxed{0.027}\)[/tex] J.
