A point charge of +3.00 ?C 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 = 1/4??₀ = 8.99 × 10⁹ N ? m²/C²)

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The work done in bringing the charges together is equal to the change in potential energy of the system. The potential energy of the system is given by:$$U = k\frac{q_1q_2}{r}$$where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.The initial potential energy of the system is zero, since the charges are initially very far apart. The final potential energy of the system is:$$U = k\frac{(3.00 \mu C)(Q)}{r}$$where r is the distance between the charges in the final configuration.The work done in bringing the charges together is:$$W = U_f - U_i = k\frac{(3.00 \mu C)(Q)}{r}$$We can solve this equation for Q:$$Q = \frac{Wr}{k(3.00 \mu C)}$$Substituting the given values, we get:$$Q = \frac{(29.0 J)(0.001 m)}{8.99 	imes 10^9 N m^2/C^2(3.00 \mu C)} = 2.15 \mu C$$Therefore, the magnitude of the charge Q is 2.15 ?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