understand that a force might act on a current-carrying conductor placed in a magnetic field
Force on a current‑carrying conductor
Objective
Understand that a force can act on a conductor that carries an electric current when it is placed inside a magnetic field.
What is happening?
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.
The magnetic force equation
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:
- $I$ = current in amperes (A)
- $\mathbf{L}$ = vector length of the wire in the field (m)
- $\mathbf{B}$ = magnetic field strength (T)
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.
Right‑hand rule (RHR) – visualising the direction
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. 🚗 ➡️ 🧲 ➡️ 👉
Quick reference table
| 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) |
Example problem
- A 0.5 m long straight wire carries a current of 3 A. It lies in a uniform magnetic field of 0.8 T that is perpendicular to the wire. Calculate the magnitude of the force.
- In a solenoid, the magnetic field is parallel to the axis. A straight segment of wire is bent into a semicircle lying in the plane of the field. What is the net force on the wire?
Exam tips
📝 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 $180^\circ$.
Analogy recap
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.
Revision
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