Magnetic Effects of Electric Current · Lesson 6 of 8
Force on a Current-Carrying Conductor in a Magnetic Field
“Put current and a magnetic field together, and the wire may literally make a move.”
• Explain why a current-carrying conductor experiences force in an external magnetic field. • Predict how reversing current or magnetic field reverses the force. • Apply Fleming’s Left-Hand Rule to determine force, field or current direction. • Explain when the magnetic force on a conductor is greatest. • Relate conventional current to the motion of positive and negative charges. • Describe selected technological and medical applications of magnetic effects.
A current-carrying wire creates its own magnetic field. If that wire is placed inside the field of a magnet, the two magnetic influences interact and the wire can move. This conversion of an electrical input into mechanical motion is one of the most useful consequences of electromagnetism.
The interaction is mutual. A current-carrying conductor can exert force on a nearby magnet, and the magnet exerts an equal and opposite force on the conductor. If the conductor is free to move, this force appears as a displacement. The direction of displacement provides evidence about the direction of the magnetic force.
Activity
To observe the force on a current-carrying aluminium rod placed in a magnetic field and investigate how its direction changes.
Suspend a short aluminium rod AB horizontally from two flexible connecting wires. Place it between the poles of a strong horseshoe magnet with the north pole below and the south pole above, so the magnetic field is vertically upward and the rod is perpendicular to it. Connect the rod in series with a battery, key and rheostat. Close the key briefly so current flows from B to A and observe the displacement.
The rod moves towards the left. Reverse current by reversing the cell connections and it moves towards the right. Restore the current direction and interchange the magnet poles so that the field points downward; the rod again reverses its displacement. These comparisons show that force direction depends on both current direction and magnetic-field direction.
| Change made | Result when other quantities are unchanged |
|---|---|
| Reverse current direction | Force direction reverses |
| Reverse magnetic-field direction | Force direction reverses |
| Reverse both current and field | Force direction remains the same |
| Increase current | Force magnitude and displacement increase |
| Use a stronger magnet | Force magnitude and displacement increase |
| Increase conductor length within field | Force magnitude and displacement increase |
The force is greatest when the current direction is at right angles to the magnetic field. In this arrangement the force is perpendicular to both. If current and field are parallel, the sideways magnetic force is absent. The chapter focuses on the perpendicular case, for which a simple hand rule identifies the force direction.
Fleming’s Left-Hand Rule
Stretch the thumb, forefinger and middle finger of the left hand so that they are mutually perpendicular. Point the forefinger along the magnetic field, conventionally from the north pole towards the south pole. Point the middle finger along conventional current. The thumb then points in the direction of force or motion of the conductor.
Assign one direction to each finger before deciding the answer: forefinger for field, middle finger for current and thumb for force. If the moving particles are electrons, first reverse their motion direction to obtain conventional current, then apply the rule.
The rule can also be used backwards. If the magnetic field and force are known, arrange the forefinger and thumb in those directions; the middle finger then gives current. The three directions must remain perpendicular. A common error is to use the right hand, which describes a different relationship.
Conventional current is defined in the direction a positive charge would move. Therefore a moving proton or alpha particle has current direction along its motion, while an electron produces conventional current opposite to its motion. This reversal must be completed before Fleming’s Left-Hand Rule is applied.
A magnetic force perpendicular to a freely moving charged particle can change the direction of its motion. Direction is part of velocity, so velocity changes even if speed stays constant. Momentum also changes because it has direction. The particle’s mass does not change merely because it moves through a magnetic field.
Problem
A conductor carries current out of the page in a magnetic field directed from left to right. Find the force direction.
- 1.Given: magnetic field points right and conventional current points out of the page.
- 2.Point the left forefinger to the right.
- 3.Point the left middle finger out of the page, towards the observer.
- 4.The left thumb points upward.
- 5.Therefore the conductor experiences an upward force.
Problem
An electron travels upward through a magnetic field directed to the right. Determine the force direction.
- 1.Given: electron motion is upward. Conventional current is opposite to electron motion, so current is downward.
- 2.Point the left forefinger to the right, along the magnetic field.
- 3.Point the middle finger downward, along conventional current.
- 4.The thumb points out of the page.
- 5.Therefore the electron experiences force out of the page. The crucial step was reversing electron motion to obtain current direction.
Problem
A positively charged alpha particle travels west and is deflected north. Determine the magnetic-field direction.
- 1.An alpha particle is positive, so conventional current is also westward.
- 2.Required: a field direction that gives northward force for westward current.
- 3.Arrange the left middle finger towards west and the thumb towards north.
- 4.The forefinger then points vertically upward.
- 5.Therefore the magnetic field is upward. A downward field would deflect the particle south instead.
Increasing current means more moving charge passes through the conductor each second, so the interaction with the external field becomes stronger. A stronger magnet supplies a stronger external field. Increasing the length of conductor inside the field gives a larger portion of current-carrying material on which the field acts. Each change therefore increases force when the others are unchanged.
Devices using forces between current-carrying conductors and magnetic fields include electric motors, generators, loudspeakers, microphones and measuring instruments. In each case, an appropriate arrangement of currents, conductors and magnetic fields produces motion or connects electrical and mechanical behaviour.
Magnetism in medicine
Electric currents in the body also produce magnetic fields. Weak ion currents travelling along nerve cells create extremely small temporary fields, roughly one-billionth of Earth’s magnetic field. Magnetic activity associated with organs such as the heart and brain is scientifically significant even though it is far too weak to move an ordinary compass.
Magnetic Resonance Imaging uses magnetic behaviour to obtain images of internal body regions. Analysis of these images supports medical diagnosis. This application shows that magnetism is not limited to bar magnets and wires in a laboratory; it also provides powerful ways to study the human body.
Do not use electron motion as though it were conventional current. Do not point the forefinger along force: it represents magnetic field. Reversing either current or field reverses force, but reversing both leaves the force direction unchanged.
Quiz
In Fleming’s Left-Hand Rule, the thumb represents
When is force on a current-carrying conductor greatest?
What happens to force direction if only current is reversed?
For an electron, conventional current is
A magnetic field changes the direction but not the speed of a freely moving charged particle. Which quantities change?
Practice Problems
- State Fleming’s Left-Hand Rule. Answer: Hold the left thumb, forefinger and middle finger mutually perpendicular. Forefinger gives magnetic field, middle finger gives conventional current and thumb gives force or motion.
- Current is out of the page and field is rightward. Find the force. Answer: Applying the left-hand rule gives an upward force.
- The current in a rod is reversed and the magnet poles are also interchanged. Predict the force direction. Answer: Each reversal alone would reverse force; reversing both cancels the directional changes, so force remains in its original direction.
- An electron moves north in a downward magnetic field. Explain the first step before applying the rule. Answer: Conventional current is opposite to electron motion, so it points south. The left-hand rule must be applied using southward current, not northward electron motion.
- Predict how displacement changes if current, magnetic-field strength and active conductor length are each increased separately. Answer: Each change increases magnetic force when other conditions remain unchanged, so the observed displacement should increase in every case.
Key Takeaways
• A current-carrying conductor placed in a magnetic field can experience a force. • Force direction depends on both current direction and magnetic-field direction. • Reversing either current or field reverses force; reversing both preserves force direction. • Force is greatest when current and magnetic field are perpendicular. • Fleming’s Left-Hand Rule assigns field, current and force to the forefinger, middle finger and thumb. • Conventional current is opposite to electron motion but along positive-charge motion. • Magnetic effects support electrical devices and medical imaging.