A current balance used to define the ampere is designed so that the current through it is constant, as is the distance between wires. Even so, if the wires change length with temperature, the force between them will change. What percent change in force per degree will occur if the wires are copper?

A group of physical characteristics known as magnetism is mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles produce a magnetic field, which then acts on other currents and magnetic moments.

We use the equation: \(F = \frac{{{\mu _0}{I_1}{I_2}L}}{{2\pi r}}\)

Noticing that the force is directly proportional to the length of the wire\(\left( L \right)\),keeping the distance\(\left( r \right)\)between two wires and currents\(\left( {{I_{1\;}}and\;{I_2}} \right)\), constant. The equation relating the change in length with the temperature\(\left( T \right)\)is:\(\Delta L = \alpha LT\). From the equation we get-

\(\begin{align}{}\Delta F \propto \Delta L \\\Delta F \propto \alpha T \\\frac{{\Delta F}}{T} \propto \alpha \end{align}\)

So, here the copper wire is: \(\alpha = 17.0 \times {10^{ - 6}}\;^\circ {C^{ - 1}}\).

Therefore, the percent value is obtained as:\(17.0{\rm{ }}x{\rm{ }}{10^{ - 4}}\% /^\circ C\).