A tiny object carrying a charge of +35 μC and a second tiny charged object are initially very far apart. If it takes 32 J of work to bring them to a final configuration in which the +35 μC 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 (Cartesian coordinate system), find the magnitude of the charge on the second object. (k = 1/4πε 0 = 8.99 × 109 N · m2/C2)

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aristocles aristocles · Answer 1 · 2019-07-07T06:11:27+02:00

Answer:

Other charge is given as

[tex]q = 0.20 \mu C[/tex]

Explanation:

Work done to bring the two charges from infinite large to finite distance is given as change in potential energy of the system of two charges

[tex]W = U_2 - U_1[/tex]

here we have

initial potential energy must be zero as it is infinite distance away initially

[tex]U_1 = 0[/tex]

now we have final energy as

[tex]U_2 = \frac{kq_1q_2}{r}[/tex]

[tex]U_2 = \frac{(9\times 10^9)(35\mu C)(q)}{(3 - 1)\times 10^{-3}}[/tex]

[tex]U_2 = (1.57\times 10^8)q[/tex]

now from above formula

[tex]32 = (1.57\times 10^8)q - 0[/tex]

[tex]q = 0.20 \mu C[/tex]