To find the difference in potential energy when a charge moves in an electric field, we use the formula for the potential energy difference:
[tex]\[ \Delta U = q \cdot E \cdot d \][/tex]
Here,
- [tex]\( q \)[/tex] is the charge, given as [tex]\( 1.3 \times 10^{-16} \)[/tex] coulombs.
- [tex]\( E \)[/tex] is the electric field strength, given as [tex]\( 3.2 \times 10^{2} \)[/tex] newtons per coulomb.
- [tex]\( d \)[/tex] is the distance moved parallel to the electric field, given as [tex]\( 1.1 \times 10^{-2} \)[/tex] meters.
By substituting the values into the formula, we get:
[tex]\[ \Delta U = (1.3 \times 10^{-16} \, \text{C}) \cdot (3.2 \times 10^{2} \, \text{N/C}) \cdot (1.1 \times 10^{-2} \, \text{m}) \][/tex]
When we multiply these values together, the numerical result is:
[tex]\[ \Delta U = 4.575999999999999 \times 10^{-16} \, \text{joules} \][/tex]
Now let's cross-check the available options:
A. [tex]\( 1.22 \times 10^{-15} \)[/tex] joules
B. [tex]\( -2.4 \times 10^{-15} \)[/tex] joules
C. [tex]\( 32 \times 10^{-15} \)[/tex] joules
D. [tex]\( -46 \times 10^{15} \)[/tex] joules
E. [tex]\( 56 \times 10^{-15} \)[/tex] joules
None of these options match our calculated potential energy difference of [tex]\(4.575999999999999 \times 10^{-16}\)[/tex] joules.
