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A straight conductor of length $L$ carrying current $I$ in uniform field $\vec{B}$ experiences force $\vec{F} = I\vec{L} \times \vec{B}$, with magnitude $F = BIL\sin\theta$. Maximum force occurs when the wire is perpendicular to the field ($\theta = 90°$); zero force when parallel ($\theta = 0°$ or $180°$). Direction follows the right-hand rule or Fleming's left-hand rule (FBI: First finger = Field, seCond = Current, thuMb = Force).

For two long parallel wires separated by distance $d$: force per unit length $F/l = \mu_0 I_1 I_2/(2\pi d)$. The defining rule: parallel currents attract, antiparallel currents repel. This force defines the ampere: 1 A produces $2 \times 10^{-7}$ N/m between wires 1 m apart.

Important extensions: (1) In a non-uniform field, a closed current loop experiences a net translational force (unlike uniform fields where forces on opposite sides cancel). (2) The magnetic force on a moving charge $\vec{F} = q\vec{v} \times \vec{B}$ is always perpendicular to velocity, doing zero work. (3) However, the magnetic force CAN do work on a current-carrying wire because the battery provides the internal energy. This distinction between single particles and current loops is conceptually deep and frequently tested.