To determine the magnitude of the difference in the potential energy of the charge moving in the electric field, we can use the formula for the work done on a charge by an electric field. When a charge [tex]\( q \)[/tex] moves a distance [tex]\( d \)[/tex] parallel to an electric field [tex]\( E \)[/tex], the work done [tex]\( W \)[/tex] on the charge is given by:
[tex]\[ W = q \cdot E \cdot d \][/tex]
Where:
- [tex]\( q \)[/tex] is the charge
- [tex]\( E \)[/tex] is the electric field strength
- [tex]\( d \)[/tex] is the distance moved in the direction of the field
Given the values:
- [tex]\( q = 6.4 \times 10^{-19} \)[/tex] coulombs
- [tex]\( E = 6.5 \times 10^4 \)[/tex] newtons per coulomb
- [tex]\( d = 1.2 \times 10^{-2} \)[/tex] meters
We substitute these values into the formula to get:
[tex]\[ W = (6.4 \times 10^{-19} \, \text{C}) \cdot (6.5 \times 10^4 \, \text{N/C}) \cdot (1.2 \times 10^{-2} \, \text{m}) \][/tex]
The work done, which equals the change in potential energy [tex]\( \Delta U \)[/tex], is:
[tex]\[ \Delta U = 4.992000000000001 \times 10^{-16} \, \text{joules} \][/tex]
We can see that the closest approximation from the given choices is:
D. [tex]\( 5.0 \times 10^{-16} \)[/tex] joules
