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Electricity & Magnetism

Magnetic Fields & Forces

A force that is zero until the charge moves, and that can never change how fast it moves once it does.

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Magnetic Fields & Forces

A force that is zero until the charge moves, and that can never change how fast it moves once it does.

35 min4 checkpoints5 simulation tasks

Introduction

Every force so far had a direction you could point to before anything moved. The magnetic force has none until the charge moves, and then it points sideways.

Predict

A positive charge moves to the right across a magnetic field that points out of the page. Which way does the magnetic force on it point?

Sideways to the motion

Try it

Make the magnetic force on the charge zero. You can change its speed or the field.

GoalNo magnetic force on the charge.

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A force that cannot do any work

Predict

The charge starts at 11.0000 m/s. Half an orbit later, with the magnetic force having pushed on it the whole way round, what does the speed readout say?

Try it

Run it until the velocity points the other way, half an orbit on. Watch the speed readout the whole time.

GoalWatch the velocity turn round.

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A force at right angles to the motion can only turn it, the way a string turns a ball swung in a circle. So the magnetic force does no work. The speed and the kinetic energy never change, only the direction.

How big the circle is

Try it

The charge goes round a circle of radius 11 m. Make the circle half as wide, using the speed or the field.

GoalHalve the radius of the circle.

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A force of constant size, always at right angles to the motion, makes uniform circular motion. So the magnetic force is the centripetal force, qvB=mv2/rqvB = mv^2/r, and the circle's radius is

r=mvqBr = \frac{mv}{qB}
Practice

A g charge carrying mC moves at m/s across a T field. What is the radius of its circle?

How long it takes

Predict

You double the charge's initial speed and leave everything else alone. What happens to the time it takes to go once round?

Try it

One lap takes 6.283 s. Make it take twice as long. You can change the speed or the mass.

GoalMake one lap take twice as long.

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The time for one lap is the circumference divided by the speed:

T=2πrv=2πmqBT = \frac{2\pi r}{v} = \frac{2\pi m}{qB}

The speed cancels. A slow charge crawls round a small circle and a fast one races round a big one, in the same time. Only mm, qq and BB set the clock.

Practice

A g charge carrying mC circles in a T field. How long does one lap take?

Crossed fields: the velocity selector

Try it

Now an electric field crosses the magnetic one, pushing the other way. At 8 m/s the charge hits a plate. Find the speed that goes straight through.

GoalSend the charge straight through the plates.

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Setting qE=qvBqE = qvB gives

v=EBv = \frac{E}{B}

with no qq and no mm in it. The device sorts a beam by speed alone, whatever the particles are made of and whichever sign they carry. J. J. Thomson used this balance in measuring the electron's charge-to-mass ratio.

Practice

A beam holds positive and negative charges of several masses, at 8, 11 and 14 m/s. E = 11 V/m and B = 1 T. Which pass undeflected?

Practice

A selector has an electric field of V/m across a T magnetic field. At what speed does a charge pass straight through?

What comes next

You stopped a magnetic force by stopping the charge, watched it turn a velocity without speeding it up, and tuned a beam through crossed fields. Next, hold the charges still and change the field instead, and something new appears that no static picture can account for.

Ideas this lesson took on

Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.

  • “The magnetic force pushes the charge along the field”
  • “A magnetic field pushes on any charge inside it”
  • “The magnetic force speeds the charge up”
  • “A faster charge takes longer to go once round”

Finished with this lesson?

Progress is stored on this device only. There is no account and nothing is sent anywhere.

Research behind this lesson

  • Maloney 1985: Given problems about electric charges moving between the pole faces of permanent magnets, students most often reasoned as though a north pole were itself positively charged and acted directly on nearby charges the way one electric charge acts on another; the next most common strategy had charges of either sign attracted to whichever pole was the stronger.
  • Maloney et al. 2001: The Conceptual Survey of Electricity and Magnetism (CSEM): a 32-question multiple-choice instrument refined over four years and administered to more than 5000 introductory students at 30 institutions. Pretest averages were 31% (calculus-based) and 25% (algebra/trigonometry-based); after instruction they reached only 47% and 44%.
  • Scaife & Heckler 2010: Across a series of written and interview studies, students began at the same low level of performance whether the field was presented as magnetic poles or as field lines, but after instruction answered correctly more often in the field-line representation: in part because more students believed charges are attracted to magnetic poles than believed charges are pushed along field lines.
  • Scaife & Heckler 2011: Simple force-direction questions put to a university course at several points in the term found that, before magnetic-force instruction, most students answered that the magnetic force on a moving charge points along the magnetic field, and that after that instruction surprising numbers began answering that the electric force is perpendicular to the electric field. The two ideas interfere in both directions, and which way depends on which was taught most recently.