Exemplo de Physics, 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

What is the missing charge?

Problema e solução em inglês, como no livro original.

Figure 18.7 shows two spheres that initially have +4 C and +8 C of charge. After an interaction (which could simply be that they touch each other), the blue sphere has +10 C of charge, and the red sphere has an unknown quantity of charge. Use the law of conservation of charge to find the final charge on the red sphere.

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Estratégia
The net initial charge of the system is $q_{initial} = + 4 C + 8 C = + 12 C$ . The net final charge of the system is $q_{final} = + 10 C + q_{red}$ , where $q_{red}$ is the final charge on the red sphere. Conservation of charge tells us that $q_{initial} = q_{final}$ , so we can solve for $q_{red}$ .
Solução
Equating $q_{initial}$ and $q_{final}$ and solving for $q_{red}$ gives

$\begin{matrix} q_{initial} & = & q_{final} \\ + 12 C & = & + 10 C + q_{red.} \\ + 2 C & = & q_{red .} \end{matrix}$
18.3

The red sphere has +2 C of charge.

Figure 18.7 Two spheres, one blue and one red, initially have +4 C and +8 C of charge, respectively. After the two spheres interact, the blue sphere has a charge of +10 C. The law of conservation of charge allows us to find the final charge $q_{red}$ on the red sphere.

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