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A long copper wire (see the picture), placed somewhere in the outer-space, having the length $L=100000 km$ and the cross section $S=1 cm^2$, comes in contact at one of its ends ($x = 0$) with a $+Q$ metal sphere of radius $R=10 cm$.

Question: Is it possible to have a flow of charge, $q(t)$, through a cross section of the wire positioned at $x = x_1$ from the origin, where $x_1>0$ and $x_1<L$? Up to the moment $t_1=x_1/c$, the quantity $q(x_1,t)$ looks to be zero because no perturbation can travel faster than the speed of light. What happens after the moment $t_1$ is no quite clear for me.

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  • $\begingroup$ Assuming the $+Q$ metal sphere is relatively small compared to the $10 \times 10^8\:\mathrm{m}$ not all that much will happen. In metals the charge carriers are electrons. Once contact between ball and wire is established, some electrons will flow from the wire to the sphere. The system ball+wire acts as a capacitor and eventually $+Q$ gets 'smeared out' over the entire system as a uniform field of charge. The question would be more interesting if $Q$ was negative and very large. $\endgroup$
    – Gert
    Commented Nov 14, 2015 at 3:24

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As the sphere comes close to the wire, it will induce a negative charge on the left end of the wire. This will cause some current in the wire even before contact is made.

With this in mind, no physical effect propagates faster than the speed of light. So the behavior of the sphere at $t=0$ cannot have any effect on $q(x_{1},t)$ before $t=\frac{x_1}{c}$.

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