# Fast-moving wires

**Electricity and Magnetism**Level 4

Consider two long parallel wires with linear charge density \(\lambda\) (charge per unit length) separated by a distance d. The wires move in the same direction (parallel to the wire direction) at a constant speed v. For what value v **in meters per second** the magnetic attraction balances the electrical repulsion? You do not need special relativity in order to solve the problem correctly. Note that even though the charge density is frame dependent, the choice of the frame does not affect the answer.

**Details and assumptions**

\[\epsilon_{0}=8.85\times 10^{-12} F/m \] \[\frac{\mu_{0}}{4\pi}= 10^{-7} H/m\]

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