Magnetic force and DC motor: Teacher's Guide

Teaching guide for the Magnetic Force & Motor simulator: explain in class the force on a current-carrying conductor in a magnetic field (Laplace's second law), the right-hand rule and the operating principle of a direct-current motor with an animated coil. Designed for physics and electrical technology teachers.

Module: Magnetic Force & Motor · Two tabs: Magnetic Force · DC Motor

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Physical phenomenon

A conductor carrying an electric current and immersed in a magnetic field $\vec{B}$ experiences a force described by Laplace's second law: the macroscopic formulation, for a conductor, of the Lorentz law that holds microscopically for a single moving charge. The force acts perpendicular to both the current and the field. For a straight conductor segment of length $L$ carrying current $I$:

$$\vec{F}=I\cdot \vec{L}\times \vec{B}$$

The magnitude is $F=B\cdot I\cdot L\cdot \sin \theta$, where $\theta$ is the angle between current and field. The force is maximum when current and field are perpendicular ($\sin \theta =1$), zero when they are parallel.

The sense is determined by the right-hand rule: thumb in the current direction, index finger in the magnetic field direction, middle finger points in the force direction.

A coil carrying current immersed in a magnetic field experiences different forces on each of its sides: these forces, balanced on opposite pairs, generate a mechanical torque rotating the coil. This is the working principle of the DC motor: adding a device (commutator + brushes) that periodically reverses the current direction in the coil keeps the rotation consistent.

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Key concepts

• Magnetic field $\vec{B}$: a vector quantity describing magnetic intensity and direction in space. Measured in tesla (T).
• Force on a conductor: proportional to $B$, $I$ and $L$, with sine dependence on the angle.
• Right-hand rule: operational tool for the force direction.
• Conventions $\odot$ and $\otimes$: dot = current/field coming out of the page; cross = going in.
• Torque on a coil: the product of forces on opposite sides times the "lever arm" between them. This is what rotates the rotor.
• Commutator: the mechanical "trick" that makes the DC motor possible: it reverses the current in the coil twice per revolution, keeping torque always in the same rotation sense.
• Maximum and zero torque: torque is maximum when the coil is parallel to the field, zero when perpendicular (unstable equilibrium position).

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How to use it in the classroom

Opening: Magnetic Force tab. Show the horizontal conductor immersed in the magnetic field (vertical arrows). Increase current $I$: the force arrow $\vec{F}$ grows proportionally. Increase field $B$: same effect. Lengthen the conductor: the same proportionality. Have students state the formula before writing it down.

Development: the right-hand rule. Reverse the sense of $I$: the force flips. Reverse the sense of $B$: same effect. Let students practise the right-hand rule at their desk, predicting where the arrow will point and then verifying it in the simulator.

Deeper exploration: DC Motor tab. Switch to the motor tab. Show the still coil with $I=0$. Increase the current: the coil starts rotating. Explain that forces act only on the two horizontal sides of the coil (perpendicular to the field), and that the resulting torque is the product of force times the lever arm.

Closing: the role of the commutator. Highlight that the rotor keeps rotating in the same sense even after passing the "vertical" position. Without the commutator (conceptually represented in the schematic), the coil would oscillate around the equilibrium position. The commutator reverses the current at the right time, keeping torque coherent.

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Real-world examples

• DC motors everywhere. Computer fans, remote-controlled toys, car window motors, low-power lifts, educational robotics: the DC motor is still the workhorse of countless applications.
• Loudspeakers. A moving coil carrying the audio signal is immersed in a permanent magnet's field: the variable current produces a variable force that vibrates the cone, exactly the law $F=BIL$ in action.
• Moving-coil microphones. Work in reverse: cone movement moves a coil in the field of a magnet, generating a current proportional to the sound.
• Analogue measuring instruments. Galvanometers and needle ammeters use the torque on a current-carrying coil in a magnetic field to deflect the needle proportionally to the current.
• Magnetic levitation trains. Use electromagnetic forces to suspend and propel the train without contact with the rails.

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Classroom discussion questions

1. The current in a conductor doubles. What happens to the force? And if the magnetic field doubles at the same time?
2. A conductor lies parallel to the magnetic field. What is the force on it? Why?
3. A DC motor without commutator: what does the coil do? Why is the commutator needed?
4. In a loudspeaker the current is alternating, not direct. Why then is it called a "linear motor" and works just as well?
5. A conductor hanging from two cables, carrying current, is immersed in a horizontal magnetic field perpendicular to the wire. What motion would you observe, and what determines its amplitude?

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Related modules

• Forces & Vectors: the force $\vec{F}=I\vec{L}\times \vec{B}$ is a vector: the right-hand rule is the geometric way to build a cross product.
• Electrostatics: the magnetic field is the dual of the electric field: where stationary charges generate $\vec{E}$, moving charges (currents) generate $\vec{B}$.