To determine the electric potential energy (U) of the point charge in the electric field, we can use the formula:
[tex]\[ U = q \cdot E \cdot d \][/tex]
where:
- [tex]\( q \)[/tex] is the charge,
- [tex]\( E \)[/tex] is the electric field (in Newtons per Coulomb, N/C),
- [tex]\( d \)[/tex] is the distance (in meters) from the charge to the source of the electric field.
Let’s go through the steps to find the electric potential energy of the point charge:
1. Convert the charge to Coulombs:
The charge given is [tex]\( 8.0 \mu C \)[/tex] (microCoulombs). We need to convert this to Coulombs (C):
[tex]\[ 1 \mu C = 1 \times 10^{-6} \, C \][/tex]
Therefore,
[tex]\[ 8.0 \mu C = 8.0 \times 10^{-6} \, C \][/tex]
2. Identify the electric field:
The electric field given is [tex]\( 1.5 \times 10^3 \, N/C \)[/tex].
3. Identify the distance:
The distance given is [tex]\( 0.050 \, m \)[/tex] (meters).
4. Plug these values into the formula for electric potential energy:
[tex]\[ U = (8.0 \times 10^{-6} \, C) \cdot (1.5 \times 10^3 \, N/C) \cdot (0.050 \, m) \][/tex]
5. Perform the multiplication:
[tex]\[ U = 8.0 \times 10^{-6} \times 1.5 \times 10^3 \times 0.050 \][/tex]
Calculate the product step by step:
[tex]\[ 8.0 \times 10^{-6} \times 1.5 \times 10^3 = 12.0 \times 10^{-3} \][/tex]
[tex]\[ 12.0 \times 10^{-3} \times 0.050 = 0.600 \times 10^{-3} \][/tex]
[tex]\[ 0.600 \times 10^{-3} = 6.0 \times 10^{-4} \, J \][/tex]
Thus, the electric potential energy of the point charge is:
[tex]\[ 6.0 \times 10^{-4} \, J \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{6.0 \times 10^{-4} \, J} \][/tex]
