Understand that a force can act on a conductor that carries an electric current when it is placed inside a magnetic field.
Imagine a line of cars (the electrons) driving along a straight road (the wire). If a magnetic field is like a set of invisible wind gusts blowing across the road, the cars feel a sideways push that can change their direction. This sideways push is the magnetic force on the conductor.
For a straight segment of wire the force is given by the cross product of the current direction and the magnetic field:
\$\mathbf{F} = I\,\mathbf{L}\times\mathbf{B}\$
Where:
In magnitude form:
\$F = I\,L\,B\,\sin\theta\$
with \$\theta\$ the angle between the wire and the field. If the wire is perpendicular to the field (\$\theta=90^\circ\$), \$\sin\theta=1\$ and the force is maximum.
Use your right hand: point your fingers along the current direction, curl them towards the magnetic field direction, and your thumb points in the force direction. 🚗 ➡️ 🧲 ➡️ 👉
| Conductor | Field orientation | Force direction (RHR) |
|---|---|---|
| Straight wire | Perpendicular to wire | Out of the page (thumb) |
| Loop in a field | Parallel to plane of loop | Inward/outward (depends on current direction) |
📝 Always check units: \$I\$ in A, \$L\$ in m, \$B\$ in T → force in N.
📝 Use the right‑hand rule: a quick way to determine the direction of \$\mathbf{F}\$.
📝 Remember \$\sin\theta\$: if the wire is not perpendicular to the field, reduce the force by \$\sin\theta\$.
📝 Diagram: draw a clear diagram with arrows for \$I\$, \$B\$, and \$F\$ before writing your answer.
📝 Check your answer: if the force is zero, either \$I=0\$, \$L=0\$, \$B=0\$ or \$\theta=0^\circ\$ or \$180^\circ\$.
Think of the current as a stream of cars moving along a road. The magnetic field is like a gust of wind blowing across the road. The cars (electrons) feel a sideways push that can change the direction of the whole road (the conductor) if the wind is strong enough. This is exactly what happens in a magnetic field – the conductor experiences a force that can make it move, bend, or vibrate.