Motor Effect

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Because a current-carrying conductor generates its own magnetic field, placing it within an external magnetic field causes the two magnetic fields to interact. As a result, the conductor experiences a mechanical force—a phenomenon known as the motor effect.

The Mathematical Model

The magnitude of the force (F) exerted on a straight wire depends on four key factors: the strength of the magnetic field (B), the electric current (I), the length of the conductor inside the field (l), and the angle (θ) between the wire and the field lines:

F = BIl sin(θ)

Where:

  • F is the magnetic force in Newtons (N)
  • B is the magnetic flux density in Teslas (T)
  • I is the conventional current in Amperes (A)
  • l is the length of the wire within the field in meters (m)
  • θ is the angle between the wire and the magnetic field vectors

The direction of the resulting force is always perpendicular to both the direction of the current and the magnetic field lines, as determined by the Right-Hand Palm Rule (or Fleming's Left-Hand Rule). Maximum force occurs when the wire is perpendicular to the field (θ = 90°), whereas no force is exerted if the wire is parallel to the field (θ = 0°).

Start by watching the introductory video below to see the motor effect in action.

 Check your understanding.
The following two video will help consolidate your understanding of the Motor Effect
The motor effect, the foundational concept in all electric motors, is easy to demonstrate with just a few simple items.

​ In this next video I not only demonstrate it qualitatively, I also show how to collect data to establish the magnetic fields of the magnets that are used in this demonstration A simple yet effective demo teachers can use the classroom to help their students
A current balance is a tool used in school to examine the motor effect. Its basically a swing which experiences a force upward on one side due to the motor effect, and a weigh on the other which counter balances it.



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Some problems
Download the sheet to practise using the formula F = Bilsinθ
Motor effect worksheet

The force between two wires

The Force Between Parallel Conductors

Since any current-carrying conductor generates its own magnetic field, placing a second current-carrying wire parallel to it creates a mutual magnetic interaction. Each conductor finds itself immersed in the magnetic field produced by the other, causing both to experience equal and opposite magnetic forces in accordance with Newton's Third Law.

Quantitative Model

The magnitude of the force per unit length (F⁄l) exerted between two parallel conductors carrying currents I1 and I2 separated by a distance r is given by:

F⁄l = μ0 I1 I2⁄2πr    &text{or}    F⁄l = k · I1 I2⁄r

Where:

  • F/l is the force per unit length in Newtons per meter (N/m)
  • I1 and I2 are the currents in each conductor in Amperes (A)
  • r is the distance between the parallel wires in meters (m)
  • μ0 is the magnetic permeability of free space (4π × 10-7 T·m/A)
  • k is the magnetic constant (μ0⁄2π = 2 × 10-7 N/A2)

Direction of Force (Attraction vs. Repulsion)

Applying the Right-Hand Grip Rule and Right-Hand Palm Rule reveals two fundamental interaction rules:

  • Parallel Currents (Same Direction): The wires attract each other.
  • Anti-parallel Currents (Opposite Directions): The wires repel each other.

Watch the video below to explore how these field interactions are modeled and how this relationship historically defined the SI unit of electric current—the Ampere.

Check your understanding

Check Your Understanding: Force Between Parallel Conductors

Question: Two long, straight parallel wires separated by a distance r carry identical currents I in opposite directions. If the distance between the wires is halved (r⁄2) and the current in both wires is doubled (2I), how does the magnitude of the force per unit length (F⁄l) between them change?

A sample problem
Picture

Two applications


Here are two applications that rely on the motor effect to work.
Useful to view, to consolidate your understanding.
A galvanometer is a device that responds to current. Its designed in such away that in recorded deflection is proportional to the current input.
This is useful, as it allows it to be calibrated so that it can act as an ammeter, or voltmeter
Classic speakers vibrate a cone, which in turn generates sound.
They use an alternating current and the motor effect to do this
 

How well do you know the motor effect?

Hopefully you have understood the concepts if you get here.
​​Test your understanding of motor effect. So do the Quiz and try to get full marks

Then check your understanding if necessary with the video
An important application of the motor effect is the working of a DC motor. This will addressed in the next lesson
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