Potential energy of point-charges: A tiny object carrying a charge of + 3.00 μC and a second tiny charged object are initially very far apart. If it takes of work to bring them to a final configuration in which the object i is at x = 1.00 mm, y = 1.00 mm, and the other charged object is at x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge on the second object. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The potential energy of point charges can be calculated using the formula:

U = k(q1q2)/r

where U is the potential energy, k is a constant, q1 and q2 are the charges on the objects, and r is the distance between the objects.

In this problem, the initial potential energy is zero because the objects are very far apart. The final potential energy is 11eb6b7b_2f91_40d6_b0cf_5703cdaad8ca_TB8274_00, which is the amount of work done to bring the objects together.

Let q2 be the charge on the second object. The distance between the objects is 2 mm (the difference in their y-coordinates). Thus, using the formula above, we can solve for q2:

11eb6b7b_2f91_40d6_b0cf_5703cdaad8ca_TB8274_00 = k(3.00 μC)(q2)/2 mm

Solving for q2 gives:

q2 = (11eb6b7b_2f91_40d6_b0cf_5703cdaad8ca_TB8274_00 * 2 mm)/(k * 3.00 μC) = 2.15 μC

Therefore, the answer is choice A.

Potential Energy of Point-Charges: a Tiny Object Carrying a Charge