Magnetic forces on moving charges

A current in a wire is just charges moving through metal. So a magnetic field should push on moving charges even when there is no wire, and it does: hold a magnet near a beam of electrons in a vacuum tube and the beam bends. This lesson applies the motor effect to beams of charged particles.

A force on a moving charge

A charged particle moving across a magnetic field feels a force. As for a wire, the force is at right angles to both the field and the direction of motion, and there is no force if the particle moves parallel to the field.

Because the force is always at right angles to the motion, it does not speed the particles up or slow them down. It changes their direction, so the beam curves.

Using Fleming’s left-hand rule for a beam

Fleming’s left-hand rule uses conventional current, which is the direction in which positive charge moves.

• For a beam of positive particles, the current is in the same direction as the particles move.
• For a beam of electrons, which are negative, the current is in the opposite direction to their motion.

So for an electron beam, first turn its direction of motion round to get the current. Then set the first finger to the field and the second finger to the current, and the thumb gives the force.

In panel A, electrons move to the right and the field points into the page. The conventional current is to the left, and the rule gives a force downwards, so the beam bends down. In panel B only the field is reversed, and the beam bends up.

Check your understanding 1 Set the current first

For the next problem, electrons travel into the page. Before using the field direction, choose the conventional-current direction and the reason.

Conventional current

Out of the pageCorrectIncorrectInto the pageCorrectIncorrect

Why this is the current direction

Current follows electron motionCorrectIncorrectElectrons carry negative chargeCorrectIncorrectField sets the current directionCorrectIncorrect

Check answer

Show answer

Conventional current is out of the page because electrons have negative charge. The field does not choose the current direction; it is used with that current to determine force.

Try it yourself 1

An electron beam into the page

Minimal support

Problem

A beam of electrons travels into the page. A magnetic field across the page points from left to right. Which way is the beam deflected?

Use the current, then read the force

Conventional current for this beam

Into the pageCorrectIncorrectOut of the pageCorrectIncorrect

Deflection at entry

Select an answerTo the leftNo magnetic forceUp the pageTo the rightDown the pageOut of the pageInto the page

1. To the left
2. No magnetic force
3. Up the page
4. To the right
5. Down the page
6. Out of the page
7. Into the page

Check answer

Hints

Hint 1

current

Which way is the conventional current for electrons moving into the page?

Hint 2

left-hand rule

Point your first finger to the right and your second finger out of the page.

Show solution step by step

1. Find the current

   Method

   The conventional current is out of the page.

   Reason

   Electrons are negative, so the current is opposite to their motion.

   Working

   Answer

   Electrons: into the page, ⊗. Current: out of the page, ⊙.

2. Apply the rule

   Method

   First finger to the right, second finger out of the page.

   Reason

   These are the field and the current.

   Working

   Answer

   The thumb points up the page.

3. State the deflection

   Working

   Answer

   The beam is deflected towards the top of the page.

Quick check

If you point your second finger along the electrons’ motion instead, you get the opposite answer. Always turn electron motion round first.

Check your understanding 2

A beam of positive particles moves to the right through a magnetic field that points into the page. Which way does it bend? Why is this the opposite of an electron beam moving the same way?

Positive-beam deflection at entry

Select an answerOut of the pageDown the pageTo the rightNo magnetic forceTo the leftInto the pageUp the page

1. Out of the page
2. Down the page
3. To the right
4. No magnetic force
5. To the left
6. Into the page
7. Up the page

Why an electron beam moving the same way bends oppositely

Electrons require a different hand ruleCorrectIncorrectCharge sign reverses the conventional currentCorrectIncorrectElectrons must move slower than positive particlesCorrectIncorrect

Check answer

Show answer

It bends upwards. For positive particles the current is in the direction of motion, to the right, and Fleming’s left-hand rule then gives an upward force. For electrons moving to the right the current is to the left, so the force is downwards. The opposite charge reverses the current, and so reverses the force.

Showing the force on an electron beam

Your teacher can show the effect with an electron-beam tube, which makes a narrow beam of electrons visible as a line or a spot on a glowing screen. The tube runs at a high voltage, so it is a teacher demonstration.

1. Note the path of the beam with no magnet nearby.
2. Bring a magnet up so that its field crosses the beam. The beam bends, showing that a force acts on the moving electrons.
3. Turn the magnet round, so the field is reversed. The beam bends the other way: reversing the field reverses the force.

Reversing the direction of the beam, or using positive particles instead of electrons, would also reverse the force, because each one reverses the conventional current.

Check your understanding 3 Plan the controlled comparison

Describe the teacher demonstration that shows magnetic deflection and tests field reversal. Name what stays fixed, what changes and the observation in each trial. Work on paper or here, then compare the complete method below; a note is optional.

Optional note from your method or comparison

Show answer

First record the beam path with no nearby magnet. With beam direction and tube settings unchanged, place a magnet so its field crosses the beam: a changed path shows deflection. Reverse only the magnet’s field direction while keeping its location and the initial beam unchanged: the deflection reverses. In the illustrated entry geometry the beam initially moving right bends down for field into the page and up for field out. Include the baseline, a crossing field, one controlled reversal and both observations. The high-voltage apparatus remains a teacher demonstration.

Check your understanding 4 Two reversals and a parallel case

Start with electrons moving right and a field into the page. Now reverse both their initial motion and the field. Predict and explain the initial force and whether the magnetic force changes their speed. Then consider a beam travelling along the field: predict its magnetic force. Work on paper or here and compare all three conclusions below; a note is optional.

Optional note from your predictions and reasoning

Show answer

Initially, electron motion right means conventional current left; field into gives force down. After both reversals, motion left means current right, and field out again gives force down. The two reversals restore the force direction, but the paths are not identical because their initial motions differ. Magnetic force stays perpendicular to local motion, so it changes direction, not speed. For motion along the field, no field lines are crossed and magnetic force is zero. Check charge-to-current conversion, both changed directions, the speed distinction and the parallel case.

Common mistakes

• Using the direction of electron motion as the current. For electrons, the current is the opposite way.
• Using the right-hand grip rule. That gives the field made by a current, not the force on it.
• Saying the magnetic force speeds the electrons up. It is at right angles to their motion, so it only changes their direction.
• Saying the thumb shows the way the particles were moving. It shows the force on them.