A charge of 3.0 μC and a second charge are initially far apart.If it takes 29 J of work to bring them to a final configuration in which the 3.0 μC is at x = 1.0 mm,y - 1.0 mm,and the other charge is at x = 1.0 mm,y = 3.0 mm,find the magnitude of the unknown charge.(The value of k is 9.0 $\times$ 10 9 N·m²/C². )

Question

Quizplus · Accepted Answer

The work done in bringing the charges together is equal to the potential energy of the final configuration. The potential energy of two charges q1 and q2 separated by a distance r is given by:$$U = k * q1 * q2 / r$$where k is the Coulomb constant.In this problem, q1 = 3.0 μC, q2 is the unknown charge, and r is the distance between the charges. We can use the given information to find the value of q2.$$U = 29 J$$$$r = \sqrt{(1.0 mm)^2 + (3.0 mm)^2} = 3.16 mm$$$$k = 9.0 * 10^9 N \cdot m^2 / C^2$$Substituting these values into the equation for U, we get:$$29 J = (9.0 * 10^9 N \cdot m^2 / C^2) * (3.0 \mu C) * q2 / (3.16 mm)$$Solving for q2, we get:$$q2 = 4.30 \mu C$$Therefore, the magnitude of the unknown charge is 4.30 μC.

A Charge of 3 ×\times× 109 N·m2/C2

A Charge of 3 $\times$ 10⁹ N·m²/C²