K323 / 2027
Electromagnetism overview

Topic 3 of 5

Magnetic force and its direction

A current-carrying conductor in an external magnetic field can experience a force. To predict its direction, identify the field and conventional current separately.

Across the gap between magnet poles, the field points from N to S. Conventional current is opposite to electron motion in a metal. A dot means out of the page and a cross means into it, for the quantity labelled beside the symbol.

Observe the force on a movable wire

Place a straight, movable conducting segment in the gap of a magnet and connect it to a suitable low-voltage d.c. supply, switch and flexible leads. Arrange the current perpendicular to the field and allow the segment to move in the predicted force direction.

Move a current-carrying wire in a magnetic gap

The upper view separates the wire's rear and front ends. Flexible leads allow its straight section to move. Brown arrows show current, teal arrows field, and purple arrows magnetic force.

A complete low-voltage conductor-force experiment and its front end viewIn the upper oblique apparatus view, a cell's positive terminal connects through a closed switch and a flexible lead to the rear end of a movable straight conductor. The conductor passes through the gap between a north pole on the left and a south pole on the right. Its front end connects through another flexible lead back to the negative terminal, making a complete circuit. Conventional current therefore travels from the rear end to the front end. The magnetic field goes right through the gap and the magnetic force on the active wire section points up. Below, a front end view along that conductor shows its current as a dot towards the reader, the same rightward field, and the same upward force. Only the magnetic force is drawn; the wire also has weight and contact or support forces. The views are schematic, with no numerical current or force scale.Oblique apparatus viewClosedswitch-+Low-voltage d.c. supplyNSRearFrontForceEnd view from the frontNSCurrent towards you

Only the magnetic force is marked. Weight and support forces still act. The lower end view represents the same wire, not an extra circuit branch.

The circuit view shows the complete current path. The front end view looks along the active segment: current comes towards the reader, the N-left/S-right gap field points right, and the magnetic force is upward.
  1. With current off, record the segment's position. Gravity and its supports still act; the magnetic force due to current in the segment is absent.
  2. Close the switch briefly and observe the movement. In the given geometry, the magnetic force is upward.
  3. Switch off before changing connections. Reverse the current while leaving the magnet arrangement fixed, then switch on and compare: the magnetic force and resulting initial movement reverse.
  4. Restore the original current direction. Reverse the magnetic field by exchanging the pole positions, keeping the wire geometry comparable. The magnetic force reverses again.

Keep the support arrangement and current magnitude comparable when comparing directions. Current-induced heating can change wire sag or tension, so observe the controlled initial response and limit heating. A movement demonstrates the effect under these conditions; it is not a calibrated measurement of force magnitude.

Use Fleming's left-hand rule

Hold the thumb, first finger and second finger of your left hand mutually perpendicular:

First finger: field
Point it along the magnetic field, from N to S across the gap.
Second finger: current
Point it along conventional current in the active conductor.
Thumb: force
It gives the magnetic force on that conductor.

The right-hand grip rule finds the field produced by a current. Fleming's left-hand rule finds the relative directions of current, an external field and force. Choose the rule for the relationship you are using.

Keep the viewpoint; change one cause

The dot means current out of the page and the cross means current into it. Teal arrows follow the field from N to S. Purple arrows show force on the wire.

Start: field right, current out

Start: field right, current out: force upThe viewpoint remains fixed. The left pole is north and the right pole is south, so the field through the gap points right. A dot in the conductor cross-section means conventional current out of the page. The purple magnetic-force arrow points up. Field, current and force are three perpendicular directions; the arrow lengths are qualitative.NSForce upCurrent towards you

Reverse the current only

Reverse the current only: force downThe viewpoint remains fixed. The left pole is north and the right pole is south, so the field through the gap points right. A cross in the conductor cross-section means conventional current into the page. The purple magnetic-force arrow points down. Field, current and force are three perpendicular directions; the arrow lengths are qualitative.NSForce downCurrent away from you

Reverse the field only

Reverse the field only: force downThe viewpoint remains fixed. The left pole is south and the right pole is north, so the field through the gap points left. A dot in the conductor cross-section means conventional current out of the page. The purple magnetic-force arrow points down. Field, current and force are three perpendicular directions; the arrow lengths are qualitative.SNForce downCurrent towards you

Reverse both

Reverse both: force upThe viewpoint remains fixed. The left pole is south and the right pole is north, so the field through the gap points left. A cross in the conductor cross-section means conventional current into the page. The purple magnetic-force arrow points up. Field, current and force are three perpendicular directions; the arrow lengths are qualitative.SNForce upCurrent away from you

Reversing either current or field reverses the force. Reversing both restores its original direction. No numerical force is represented by arrow length.

All four panels use the same front viewpoint. Reversing current alone or field alone reverses the force. Reversing both restores its original direction.
Controlled comparisons for the movable wire; current and field are perpendicular.
Current in the wireGap fieldInitial magnetic-force direction
Out of the pageRightUp
Into the pageRightDown
Out of the pageLeftDown
Into the pageLeftUp

Compare the first and second rows to isolate current reversal. Compare the first and third to isolate field reversal. The last row changes both and returns to the original force direction.

Find a missing direction

The force is downward and the field is rightward

Put your thumb down and first finger right. The second finger points into the page, so that is the required conventional-current direction.

Alternatively, if current is out of the page and force is upward, those two directions require the field to point right. Any two known perpendicular directions can determine the third.

The examples use perpendicular current and field. If a straight segment's current is parallel or opposite to the field, the magnetic force on that segment is zero in this model. Do not force three non-perpendicular directions into the perpendicular-case hand rule.

Optional check In a fixed front view, a wire carries current out of the page in a magnetic field directed right. Its magnetic force is upward. What is the force direction if both the current and the field are reversed?
In a fixed front view, a wire carries current out of the page in a magnetic field directed right. Its magnetic force is upward. What is the force direction if both the current and the field are reversed?

A force on a charged-particle beam

A magnetic field can deflect moving charges even when they are not confined to a metal wire. In an appropriate evacuated-tube demonstration, an electron beam produces a spot on a fluorescent screen.

  1. With the applied magnetic field off, record the spot's reference position.
  2. Apply a magnetic field perpendicular to the beam's initial motion. The spot shifts, showing that the beam has been deflected.
  3. Keep the beam conditions and tube position fixed and reverse the field. The spot shifts in the opposite direction relative to the reference.

Do not infer a field effect from changing the beam's settings at the same time. The tube and screen provide evidence of deflection; a drawn curved path is a model of the motion between emission and detection.

For positive charges, conventional current follows their motion. For electrons, it points opposite to their motion. Use that conventional-current direction with Fleming's left-hand rule.

The same initial motion, opposite charges

Both beams initially move right. Crosses mean magnetic field into the page. The amber trace shows motion; the purple arrow shows the force at entry only.

Positive charges: initial force upwards

Positive charges: initial force upwardsA positive-charge beam enters a region from the left, initially moving right. Cross marks denote a magnetic field into the page. At the entry point, a purple force arrow points up, perpendicular to the initial motion. The qualitative trace subsequently curves upwards; its motion arrow is tangent to the curve. Only the initial force is drawn. The force changes direction as the velocity turns, and the trace radius is not a supplied measurement.InitialmotionInitialforceField into the page

For positive charges, conventional current follows the beam's motion.

Electrons: initial force downwards

Electrons: initial force downwardsAn electron beam enters the same field region from the left, initially moving right. The magnetic field is into the page. Conventional current is opposite to electron motion, so the initial magnetic force points down. A purple arrow at the entry point shows that local initial force. The trace curves downwards with a tangent motion arrow. Its radius is schematic; matching drawing sizes across these two panels do not claim equal physical radii for different particles.InitialmotionInitialforceField into the page

For electrons, conventional current is opposite to the beam's motion.

These are qualitative traces, not measured radii. As a beam turns, the force stays perpendicular to its instantaneous motion; it does not keep one fixed upward or downward direction.

Both beams initially move right in a field directed into the page. Positive charges initially experience force up, while electrons initially experience force down. The force arrows shown refer to the initial motion.

Account for the charge sign

An electron beam moves right

The field is into the page. The electrons' motion is rightward, so the conventional-current direction is leftward. The left-hand rule then gives an initial force downward.

With the same initial motion but the field reversed out of the page, the initial force is upward. A positive beam moving right would deflect the opposite way in each case.

Reversing the motion of the same type of charged particles through the same field reverses the conventional-current direction and hence the initial force. For example, electrons initially moving left through the into-page field experience an initial upward force. A suitable comparison requires a beam arrangement that sends them the opposite way; simply reversing an electron gun's supply does not make the same electrons travel backwards through it.

If both the same-charge beam's initial travel and the field are reversed, the initial force returns to its original direction. Compared with the right-moving electrons in an into-page field, left-moving electrons in an out-of-page field also have an initial downward force.

As a beam curves, its instantaneous direction changes and the magnetic force remains perpendicular to that motion. A force drawn downward at entry does not stay vertically downward everywhere along the path. A beam moving parallel to the magnetic field has no magnetic deflection in this simple model.

Optional check An electron beam initially moves right through a magnetic field directed into the page. What is its initial magnetic deflection in this view?
An electron beam initially moves right through a magnetic field directed into the page. What is its initial magnetic deflection in this view?