Map magnetic fields with a compass and explain the interactions between moving charges, currents and magnetic fields, including induction, motors and generators

Learning goal: Define the direction of a magnetic field by the equilibrium direction of a compass needle and represent fields with field-arrow diagrams, explain why bar, horseshoe and circular magnets have differently shaped fields, describe how moving charges and currents create magnetic fields and how magnetic materials get their fields, state the factors that determine the magnetic force on a moving charge and the path it follows, explain electromagnetic induction and its use in generators and motors, and connect changing fields to electromagnetic waves.

What a magnetic field is and how it is mapped. At any point, the magnetic field points the way the north end of a small compass settles when the compass is placed there. Move the compass from place to place, draw an arrow at each position, and you have a field-arrow diagram: the compass gives the direction at each point. It does not measure strength directly (how briskly the needle swings also depends on how it started, friction and Earth's field), so strength is shown by drawing arrows longer where the field is known to be stronger, such as close to the poles, or measured with a magnetic field sensor. (As with electric fields, continuous field-line diagrams are a separate representation not used in this course.) In this course magnetic field strength is not calculated, but it is important that a greater magnetic field results in a larger magnetic force on magnetic objects, and on moving charges, placed in it. Around a bar magnet the arrows point away from the north pole, curve around the sides and point into the south pole, and they are longest near the poles. A horseshoe magnet is a bar bent so that its two poles face each other across a gap; between the poles the arrows are long, nearly straight and parallel, showing a strong, almost uniform field in the gap, with shorter arrows (a weaker field) elsewhere. A circular (ring) magnet magnetized through its thickness has one flat face as north and the other as south, so the field passes through the hole and loops around the outside; the shape of every field follows from where the poles are and how far apart they sit. Earth itself has a field, detected from the orientation of compass needles: the north end of a compass points toward Earth's geographic north because that region behaves as a magnetic south pole, and the field is produced by electric currents in Earth's interior. That field deflects charged particles arriving from the Sun and has guided navigation for centuries.

Electricity and magnetism are one interaction. Magnetic forces are closely related to electric forces; although they appear distinct, they are two faces of one electromagnetic interaction. Any moving charge, and so any electric current, is surrounded by a magnetic field; a compass placed near the wire swings when the current is switched on, and that motion is the evidence of the field. For a straight wire the field arrows form circles around the wire, and a right-hand rule gives the sense: point the right thumb along the conventional current and the fingers curl in the direction of the field. Coiling the wire into a solenoid adds the loops' fields to make a field like a bar magnet's, stronger with more turns and more current. The motion of electrically charged particles in atoms also produces magnetic fields. In most materials the atomic fields are randomly oriented and cancel; in magnetic materials such as iron, the subatomic fields align over regions, and when the regions themselves are aligned the material shows a macroscopic magnetic field. Heating or hammering can undo the alignment.

Force on a moving charge. A magnetic field pushes on a charged particle only when the particle is moving. The magnetic force is at right angles both to the field and to the particle's velocity; a second right-hand rule gives its direction (fingers along the velocity of a positive charge, curl them toward the field, the thumb gives the force; reverse it for a negative charge). How large the force is depends on four things: how fast the particle moves, how much charge it carries, how strong the field is, and the angle its velocity makes with the field. It is largest when they are perpendicular and there is no force at all on a particle moving parallel to the field. A stationary charge feels no magnetic force. Because the force is always perpendicular to the motion, it does no work and changes the direction of the velocity without changing the speed; by Newton's second law the particle is continually deflected, so a charge moving across a uniform field follows a circle, and one with a velocity component along the field follows a spiral. A more massive particle at the same speed and charge curves more gently (same force, less acceleration), a faster one also curves more gently, and a particle of opposite charge curves the opposite way. Calculations of the magnetic force are not required at this level; the reasoning about direction and path is.

Induction: changing magnetic fields make electric fields. Wherever a magnetic field is changing, an electric field appears. Put a closed loop of wire in such a region and that electric field pushes charges around the loop: an induced current. A changing field through a loop can be produced by moving a magnet toward or away from it, moving the loop, or turning either one, or, with nothing moving at all, by changing the current in a nearby electromagnet; what matters is that the amount of magnetic field passing through the loop changes. (When it is the wire that moves through a steady field, the charges in the wire are moving charges in a magnetic field, and the magnetic force on them drives the current; both descriptions predict the same current.) A steady magnet beside a stationary coil induces nothing, and a closed circuit is needed for a current to flow. The induced voltage is larger for a stronger magnetic field, a faster change and more loops in the coil; the induced current also depends on the resistance of the circuit. Calculations of induced current are not required at this level. The link works both ways: a magnetic field that changes produces an electric field, and an electric field that changes produces a magnetic field. Each field keeps regenerating the other, so a disturbance can travel on its own: accelerating charges, such as electrons surging back and forth in an antenna, send out linked electric and magnetic fields that travel at the speed of light with no medium needed. That traveling pattern is an electromagnetic wave.

Motors, generators and other devices. Electric and magnetic effects working together are what make generators (mechanical energy in, electrical energy out) and motors (electrical energy in, mechanical energy out) possible, along with every device that sends or picks up electromagnetic waves. A generator turns a coil in a magnetic field (or a magnet inside a coil); the field through the coil keeps changing, so a current is induced, and the mechanical work done to turn it is what becomes electrical energy, which is why a hand-cranked generator gets harder to turn when a lamp is connected. A motor is the reverse: current in a coil placed in a magnetic field experiences magnetic forces on its moving charges that turn the coil, and a commutator or electronic switching reverses the current each half turn so the coil keeps rotating. A loudspeaker is a motor that pushes a cone back and forth; a microphone is a generator in which the moving coil induces the signal current. Coils of wire and magnets are therefore found throughout speakers, microphones, generators and motors.

Misconception: a magnet near a wire is enough to make a current. Only a change in the amount of magnetic field passing through the coil induces a current: moving the magnet toward or away from the coil, turning either one so that the field through the coil changes, or switching an electromagnet on or off all work, while a steady magnet at rest beside the coil does nothing. Motion alone is not enough: spinning a bar magnet about its own long axis, or sliding a coil sideways while it stays inside a uniform field, leaves the field through the coil unchanged and induces nothing. A second misconception is that magnetic force speeds particles up: it only turns them, so a magnetic field alone cannot increase a particle's kinetic energy.

Investigation: fields from a magnet and from a current, and an induced current. Materials: a bar magnet, a horseshoe magnet, a ring magnet, a second bar magnet that is noticeably weaker or stronger, a small compass, paper, modeling clay, a 1.5 V cell, a flashlight bulb in a holder to limit the current, insulated wire, a coil of at least 50 turns and a second coil with about half as many turns, a galvanometer or microammeter (or a zero-center milliammeter). Part 1: lay the bar and horseshoe magnets flat on paper; stand the ring magnet on its edge in a lump of modeling clay so that the axis through its hole lies level with the paper (a compass needle shows only the horizontal part of the field, and a ring lying flat sends much of its field straight up and down, which the compass cannot map); place the compass at twelve positions around each magnet and draw an arrow at each; compare the three maps and explain the differences by the positions of the poles. Part 2: connect cell, bulb and a straight length of wire in series; lay the wire north-south over the compass; close the circuit for no more than three seconds and record which way the needle swings; reverse the cell and repeat; predict the direction with the right-hand rule before each trial. Part 3: connect the coil to the galvanometer; push the bar magnet in, hold it still, pull it out, then repeat faster and with the magnet reversed, recording the sign and size of each deflection; then change one factor at a time, repeating the same push at the same speed with the other magnet and again with the smaller coil. A result that supports the claims: the compass arrows loop from north to south pole and are most decisive near the poles; the needle swings the predicted way and reverses with the current; the galvanometer deflects only while the magnet moves, more for faster motion, for the stronger magnet and for the coil with more turns, and in the opposite sense for withdrawal or a reversed magnet. What the models cannot show: the compass map gives directions but no numerical field strength, and the coil test shows when a current is induced but not the electric field that drives it. Safety: never connect a wire directly across a cell without the bulb (it heats quickly); keep magnets away from phones and credit cards; the whole activity uses one 1.5 V cell and nothing higher.

Worked example 1 — reading a compass map. A compass placed just beyond the north pole of a bar magnet points away from the magnet; just beyond the south pole it points toward the magnet; above the middle it points from the north end toward the south end. Joining the arrows gives loops leaving the north pole and entering the south pole. Farther from the magnet the needle settles less decisively and Earth's field increasingly wins, evidence that the magnet's field weakens with distance. A horseshoe magnet's map shows nearly parallel arrows crossing the gap between its facing poles and little elsewhere; a ring magnet's shows arrows passing through the hole from one face and returning around the outside.

Worked example 2 — direction of a wire's field. A vertical wire carries conventional current upward. Right-hand rule: thumb up, fingers curl counterclockwise seen from above, so the field arrows circle the wire counterclockwise. A compass placed east of the wire points north-ish, one placed west points south-ish; reversing the current reverses both. This is exactly the swing seen in Part 2 of the investigation.

Worked example 3 — path of a charged particle. A proton moves east through a magnetic field pointing north. Velocity and field are perpendicular, so the force is at its maximum and perpendicular to both: by the right-hand rule (fingers east, curl toward north, thumb up), the force is upward. The proton is continually deflected and, with no velocity component along the field, moves in a circle. An electron with the same velocity is pushed downward and circles the opposite way; an alpha particle (twice the charge, four times the mass) at the same speed feels twice the force but has four times the inertia, so its circle is twice as wide as the proton's. A particle moving north, parallel to the field, feels no force and continues in a straight line.

Worked example 4 — designing a generator. To light three flashlight bulbs in series, a hand-cranked generator needs a large changing field through many turns: a coil of several hundred turns wound on a spool, a strong magnet spinning inside it (or the coil spinning between the poles of a horseshoe magnet), and a crank geared to turn it fast. If the bulbs glow only dimly, the design choices that raise the induced voltage are more turns, a stronger magnet, faster rotation or a closer coil-magnet spacing; each raises the current too, provided the extra turns of wire do not add too much resistance. In terms of induction: the rotation makes the magnetic field through the coil change continuously, the changing field creates an electric field in the wire, and that field drives the current through the bulbs (when it is the coil that spins, the magnetic force on the charges in the moving wire does the same job).

Representation task: three field maps and two right-hand-rule predictions. Draw field-arrow diagrams (at least twelve arrows each, longer where the field is stronger) for a bar magnet, a horseshoe magnet and a ring magnet, and write one sentence for each explaining its shape from the positions of its poles. Then draw a wire with current into the page and add the circular field arrows with their sense, and draw a positive charge moving to the right through a field pointing into the page with the force arrow shown, stating the rule you used for each.

Independent performance: an induction investigation and a device explanation. Carry out Parts 2 and 3 of the investigation and write a report. Success criteria: a table of trials recording the direction and relative size of every compass swing and galvanometer deflection, with the right-hand-rule prediction made before each trial; a claim about when a current is induced and what three factors affect its strength, supported by your data; an explanation of why holding the magnet still inside the coil gives zero deflection; a labeled design plan for a generator to light three bulbs in series, explaining in terms of electromagnetic induction how each design feature contributes, and stating what you would change if it lit only one; and a paragraph comparing a motor and a generator as energy converters, including where the energy comes from when a generator lights a lamp.