Final answer:
The change in electrical potential energy when a negatively charged particle moves towards a fixed positively charged particle can be calculated using Coulomb's law. We calculate the potential energy at two distances and find their difference to determine the change. The provided answer options do not match the result from these calculations, suggesting an error in the given question or options.
Step-by-step explanation:
The question asks about the change in electrical potential energy when a charged particle moves in the presence of another fixed charged particle. To find the change in potential energy, we use the formula for electric potential energy which is U = k * Q1 * Q2 / r, where U is the potential energy, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q1 and Q2 are the charges, and r is the distance between them.
We calculate the potential energy at the initial position (2.5 cm = 0.025 m) and at the final position (1.5 cm = 0.015 m) after the first particle has moved 1.0 cm towards the second particle. The change in electric potential energy is the difference between these two values:
- Initial potential energy, U_i = (8.99 x 10^9 Nm^2/C^2) * (-1.5 x 10^-9 C) * (2.5 x 10^-9 C) / 0.025 m
- Final potential energy, U_f = (8.99 x 10^9 Nm^2/C^2) * (-1.5 x 10^-9 C) * (2.5 x 10^-9 C) / 0.015 m
The change in potential energy, ∆U, is U_f - U_i. Performing these calculations will show that the correct answer is not present in the given options; hence there's likely an error in the question or the options provided.