Quick questions on Force on current-carrying conductors: HSC Physics Module 6

A wire of length $L$ carrying current $I$ in a uniform magnetic field $\vec{B}$ experiences a force:

Two long, straight, parallel wires carrying currents $I_1$ and $I_2$ separated by a distance $r$ exert magnetic forces on each other. The magnetic field at wire 2 due to wire 1 (at distance $r$) is:

This is sometimes summarised as "parallel currents attract, antiparallel currents repel," the reverse of the rule for electric charges.

The pre-2019 SI definition of the ampere used parallel wires. One ampere was defined as the current in each of two infinite, parallel wires 1 m apart in vacuum that would produce a force per unit length of:

A conducting bar of length $L = 0.30$ m slides along two rails carrying a current $I = 200$ A. It sits in a field $B = 0.50$ T perpendicular to both the bar and the rails. The force on the bar is:

Quoting $F = BIL$ when the wire is at an angle other than 90 degrees costs marks.

This formula uses conventional current (positive charge flow). The right-hand rule applies directly; you do not need to flip it for the electron-flow direction.

Both wires feel the same magnitude of force, even if their currents have different magnitudes. Both wires have the same $F/L = \mu_0 I_1 I_2 / (2 \pi r)$.

The parallel-wire force is magnetic and depends on currents (charge flow), not on net charge. Two stationary wires with no current exert no force on each other, regardless of how much net charge they carry per unit length (ignoring electrostatic effects).

Antiparallel parallel wires repel. The right-hand rule confirms: reversing one current flips the force on that wire.