To determine the potential difference between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we start by using the relationship between electric potential difference (voltage), charge, and change in electric potential energy. The formula for electric potential difference [tex]\( V \)[/tex] is given by:
[tex]\[
V = \frac{\Delta E}{q}
\][/tex]
where:
- [tex]\( \Delta E \)[/tex] is the change in electric potential energy (in Joules),
- [tex]\( q \)[/tex] is the charge (in Coulombs).
We are given:
- The charge [tex]\( q = -3.72 \times 10^{-4} \, \text{C} \)[/tex],
- The change in electric potential energy [tex]\( \Delta E = 0.218 \, \text{J} \)[/tex].
Substituting the given values into the formula, we get:
[tex]\[
V = \frac{0.218 \, \text{J}}{-3.72 \times 10^{-4} \, \text{C}}
\][/tex]
Performing the division, we find:
[tex]\[
V = -586.0215053763441 \, \text{V}
\][/tex]
So the potential difference between point [tex]\( A \)[/tex] and point [tex]\( B \)[/tex] is:
[tex]\[
-586.0215053763441 \, \text{V}
\][/tex]
The negative sign indicates that the electric potential at point [tex]\( B \)[/tex] is lower than the electric potential at point [tex]\( A \)[/tex].
