A point charge of +3.00 μC and a second charge Q are initially very far apart.If it takes $29.0 \mathrm {~J}$ of work to bring them to a final configuration in which the $+ 3.00 - \mu \mathrm { C }$ charge is at the point x = 1.00 mm,y = 1.00 mm,and the second charge Q is at the point x = 1.00 mm,y = 3.00 mm,find the magnitude of the charge Q.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

The work done to bring two charges from infinity to a certain distance is given by the formula $W = \frac{kq_1q_2}{r}$, where $W$ is the work done, $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$), $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. Given $W = 29.0 \, \text{J}$, $q_1 = +3.00 \, \mu\text{C} = 3.00 \times 10^{-6} \, \text{C}$, and $r = 2.00 \, \text{mm} = 2.00 \times 10^{-3} \, \text{m}$ (the distance between the points in the y-direction), we can solve for $q_2$:$$29.0 = \frac{(8.99 \times 10^9) \times (3.00 \times 10^{-6}) \times q_2}{2.00 \times 10^{-3}}$$Solving for $q_2$ gives $q_2 = 2.15 \, \mu\text{C}$.

A Point Charge of +3 29.0 J29.0 \mathrm {~J}29.0 J Of Work to Bring Them to a Final Configuration in Q

A Point Charge of +3 $29.0 \mathrm {~J}$ Of Work to Bring Them to a Final Configuration in Q