To solve for the potential difference between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we need to follow these steps:
1. Identify the given values:
- The charge [tex]\( q = 7.3 \times 10^{-15} \)[/tex] coulombs.
- The potential energy at point [tex]\( A \)[/tex], [tex]\( U_A = 3.5 \times 10^{-12} \)[/tex] joules.
- The potential energy at point [tex]\( B \)[/tex], [tex]\( U_B = 1.3 \times 10^{-12} \)[/tex] joules.
2. Calculate the change in potential energy [tex]\( \Delta U \)[/tex]:
[tex]\[
\Delta U = U_A - U_B
\][/tex]
Substituting the given values:
[tex]\[
\Delta U = 3.5 \times 10^{-12} \, \text{J} - 1.3 \times 10^{-12} \, \text{J} = 2.2 \times 10^{-12} \, \text{J}
\][/tex]
3. Calculate the potential difference [tex]\( \Delta V \)[/tex]:
The potential difference [tex]\( \Delta V \)[/tex] is given by the formula:
[tex]\[
\Delta V = \frac{\Delta U}{q}
\][/tex]
Substituting the values for [tex]\( \Delta U \)[/tex] and [tex]\( q \)[/tex]:
[tex]\[
\Delta V = \frac{2.2 \times 10^{-12} \, \text{J}}{7.3 \times 10^{-15} \, \text{C}}
\][/tex]
4. Simplify the expression for [tex]\( \Delta V \)[/tex]:
[tex]\[
\Delta V = 3.0 \times 10^2 \, \text{V}
\][/tex]
Therefore, the potential difference between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\( 3.0 \times 10^2 \)[/tex] volts.
Hence, the correct answer is:
[tex]\[
\boxed{3.0 \times 10^2 \, \text{V}}
\][/tex]
Or in terms of the given multiple choice options, the correct answer is:
[tex]\[
\boxed{\text{B. } 3.0 \times 10^2 \text{ volts}}
\][/tex]
