Electric vs Magnetic Field: The Difference

The distinction, stated once

Both are vector fields. Both fill space, both are drawn with arrows, both act on charge. Three things separate them, and everything else on this page follows from these three.

Motion. An electric field pushes a charge whether it is moving or standing still. A magnetic field exerts no force at all on a charge at rest. Put $v = 0$ into $F_B = qvB\sin\theta$ and the force is gone.

Direction. The electric force lies along the field, forward for a positive charge and backward for a negative one. The magnetic force lies perpendicular to the field and perpendicular to the velocity, which means it is never along either input.

Energy. Because the magnetic force is always perpendicular to the direction of travel, it does no work. It steers. The electric force is under no such restriction, and changing a charge's speed is the ordinary thing it does.

The AP Physics 2 CED puts the second one plainly at EK 12.2.B.2.ii: the direction of the force exerted by a magnetic field on a moving charged object is perpendicular to both the direction of the magnetic field and the velocity of the charge, as defined by the right-hand rule. The third one is not stated in the CED in those words, but it follows in one line from the second, and the derivation is in the section below.

EK 12.2.B.3 supplies the rule for a region that has both: a moving charged object experiences independent forces from each field. Not a combined field, not an average. Two forces, computed separately and added as vectors.

Side by side

Two rows do the heavy lifting.

The force on a charge at rest row is the fastest experimental test there is. Suspend a charged pith ball and see whether it swings. If it does, there is an electric field. A magnetic field would leave it hanging.

The can it change speed row is the one that pays on a free response, because it converts a messy geometry question into an energy statement you can write down before doing anything else.

The field lines row is a real structural difference rather than a drawing convention. Electric field lines terminate on charges, so a closed surface can have more lines leaving than entering. Magnetic field lines close on themselves, so whatever goes in comes back out. That difference is the entire content of two of Maxwell's equations, and it belongs to electric flux vs magnetic flux rather than here.

The case that separates them: one charge, four states of motion

Set up a region that contains an electric field of $1.0 \times 10^4 \ \mathrm{N/C}$ and a magnetic field of $0.30 \ \mathrm{T}$, and drop the same charge $q = +4.0 \ \mathrm{\mu C}$ into it four times, in four states of motion. The speed, when it is moving, is $5.0 \times 10^4 \ \mathrm{m/s}$.

One column never moves. The other is zero three times out of four and depends on a direction the electric force does not care about.

Those are the three angles the AP Physics 2 CED lets you compute with. The boundary statement on Topic 12.2 restricts quantitative treatment of the magnetic force on a moving charge to angles of 0, 90 and 180 degrees between the velocity and the magnetic field, with qualitative analysis permitted at other angles. That is a genuinely useful restriction: it means a Physics 2 numerical answer is almost always either $qvB$ or zero.

Note what the table does not show. In the third row both forces are present at once, and their directions are set by different rules, so they are not necessarily parallel and you cannot add the numbers $0.040$ and $0.060$ without drawing the vectors. That is what EK 12.2.B.3 means by independent forces.

The magnetic force does no work, and that is the fact worth carrying

This is the single most useful consequence of the perpendicularity rule, and it is worth being able to derive rather than recall.

Work is $W = Fd\cos\theta$, with $\theta$ the angle between the force and the displacement. A small displacement is along the velocity. The magnetic force is perpendicular to the velocity at every instant, by EK 12.2.B.2.ii. So the angle between force and displacement is 90 degrees, the cosine is zero, and the work is zero at every instant of the motion.

Zero work means no change in kinetic energy, which means no change in speed. A magnetic field can bend a charged particle through any angle, hold it in a circle indefinitely, or reverse it, and the speed it started with is the speed it keeps.

The electric force has no such constraint. In a uniform field it is constant in magnitude and direction, so a charge released in it accelerates in a straight line exactly as a mass does in gravity, and gains kinetic energy the whole way.

Three things this fact settles immediately.

• A charged particle entering a uniform magnetic field perpendicular to the field moves in a circle at constant speed. Setting $qvB = mv^2/r$ gives $r = mv/(qB)$, and that is a derivation the exam expects rather than a printed formula.
• "How fast is it going after the magnetic field bends it?" has the same answer as "how fast was it going before?" every single time.
• Any energy question in a region with both fields is answered by the electric force alone. The magnetic term contributes nothing to $\Delta K$, so you can drop it from the energy equation and keep it only in the force diagram.

The CED does not print this conclusion in a single essential-knowledge statement, so cite the perpendicularity and then the definition of work rather than asserting it bare on a free response. The magnetic force entry sets out both forms of the force law.

Sources and shapes: where the lines start and where they stop

The difference in what makes each field is as sharp as the difference in what each field does.

Electric fields come from charge. EK 10.3.A.1 in AP Physics 2 says electric fields may originate from charged objects. One charge is enough, and its sign decides the direction: away from isolated positive charge, toward isolated negative charge, per EK 10.3.A.2.ii. Because lines start on positive charge and end on negative charge, an isolated positive charge is a place where field lines simply begin.

Magnetic fields have no equivalent starting point. EK 12.1.A.1.i states that magnetic fields can be produced by magnetic dipoles or combinations of dipoles, but never by monopoles, and EK 12.1.A.1.ii adds that magnetic dipoles have north and south polarity. The smallest possible magnetic source already has two ends. Break a bar magnet in half and you get two magnets, not a free north pole.

The consequence is EK 12.1.A.2.i: magnetic field lines form closed loops. EK 12.1.A.2.ii spells out the bar magnet case, with the external field pointing away from one end, defined as the north pole, and returning to the other end, defined as the south pole. AP Physics C: Electricity and Magnetism goes further at EK 12.1.A.3 and names the law that says so, Gauss's law for magnetism, adding at EK 12.1.A.3.i that it is Maxwell's second equation.

There is a second source of magnetic field with no electric counterpart. EK 12.2.A.1 says a single moving charged object produces a magnetic field, and EK 12.2.A.1.ii puts its direction perpendicular to both the object's velocity and the position vector from the object to the point, again by the right-hand rule. So motion appears twice in the magnetic story: a moving charge makes a magnetic field, and a magnetic field acts only on moving charges. Neither half has an analogue on the electric side.

One consequence worth holding on to: whether you see a magnetic field at all can depend on your reference frame, because whether a charge is moving depends on who is watching. AP does not ask you to compute that, but it is why the two fields are ultimately one thing viewed from two seats.

Directions, and the conventions the AP exam assumes

The electric force direction needs no rule beyond a sign. Write $\vec{F}_E = q\vec{E}$, keep the sign of $q$, and you are done: a positive charge is pushed along the field, a negative charge against it. Nothing is perpendicular to anything.

The magnetic force needs a hand, because there are two directions perpendicular to both $\vec{v}$ and $\vec{B}$ and only one of them is right. Point your fingers along the velocity, curl them toward the field, and your thumb gives the force on a positive charge. For a negative charge, run the rule as stated and then reverse the answer as a written step, rather than switching hands. The right-hand rule entry sets out all three of its AP uses.

Two conventions from the equation sheet ride underneath every one of these problems, and both are printed in the exam conventions box.

• Current is conventional current. The field around a wire, and the force on it, are worked out with positive charge flowing, not with electrons. Using electron flow inverts every direction on the page.
• The electric potential is zero at an infinite distance from an isolated point charge. That fixes the zero for everything on the electric side and has no magnetic counterpart, since there is no magnetic charge to measure a potential from.

One more asymmetry in the algebra. The magnitude equations carry an angle on the magnetic side and not on the electric side: $F_B = qvB\sin\theta$ against $\lvert \vec{F}_E \rvert = qE$. If your electric force expression has grown a $\sin\theta$, or your magnetic one has lost it, check which field you are working with.

What the AP Physics 2 sheet prints for each

The AP Physics 2 sheet keeps the two in separate blocks, and comparing them is instructive.

The Electricity block gives the field a definition, $\vec{E} = \vec{F}_E/q$, a point-charge source equation, $\lvert \vec{E} \rvert = k \lvert q \rvert / r^2$, and a link to potential, $\lvert \vec{E} \rvert = \lvert \Delta V / \Delta r \rvert$.

The Magnetism block gives no definition of $\vec{B}$ at all. What it prints is the two force laws, $F_B = qvB\sin\theta$ and $F_B = I\ell B\sin\theta$, one source equation, $B = \mu_0 I/(2\pi r)$ for a long straight wire, and then flux and induction. That is the whole block.

Three things follow, and they are worth knowing before you sit down.

There is no printed equation for the field of a bar magnet, a current loop or a single moving charge. Those are described qualitatively in AP Physics 2 and computed in AP Physics C: Electricity and Magnetism, where the Biot-Savart law appears.

The tesla is defined through a force law rather than given its own line. Rearranging $F_B = I\ell B$ gives $B = F/(I\ell)$, so one tesla is one newton per ampere metre. The Physics 2 sheet lists the tesla in its unit symbols table and leaves the relation to you.

The two field constants sit next to each other in the constants box. Vacuum permittivity $\varepsilon_0 = 8.85 \times 10^{-12} \ \mathrm{C^2/(N \cdot m^2)}$ governs the electric side; vacuum permeability $\mu_0 = 4\pi \times 10^{-7} \ \mathrm{(T \cdot m)/A}$ governs the magnetic side. The Coulomb constant is printed as $k = 1/(4\pi\varepsilon_0) = 9.0 \times 10^9 \ \mathrm{N \cdot m^2/C^2}$, and the magnetic equations carry $\mu_0/(2\pi)$ instead of a named constant. The two constants have their own comparison at permittivity vs permeability.

When it costs a mark

Giving a magnetic force to a stationary charge. The most common single error on this pair. If $v = 0$, then $F_B = 0$, no matter how strong the field is. A charge sitting in a magnet's field feels nothing from it.

Drawing the magnetic force along the field. It is perpendicular to the field, always. A force arrow lying in the plane of $\vec{v}$ and $\vec{B}$ is wrong before you check its sign, and a grader can see that from across the room.

Using the angle from the wrong pair of vectors. In $F_B = qvB\sin\theta$, the angle is between the velocity and the field. Not between the velocity and the force, not between the field and any surface.

Letting a magnetic field change a speed. If a worked answer has a particle leaving a magnetic field faster than it entered, something upstream is wrong. Use it as a check on the whole problem.

Adding the two force magnitudes. In a region with both fields, the forces are independent and generally point in different directions, so $0.040 + 0.060$ is not a net force. Draw the two vectors and add them properly.

Naming the right-hand rule instead of using it. The AP Physics 2 CED is explicit that saying the force is in a given direction "because of the right-hand rule" is not enough to earn a point. State the two input directions and the sign of the charge, then the result.

Where they meet, and what to read next

The two fields are not independent subjects, and the places where they touch are the places the exam likes.

A changing magnetic flux produces an electric field, which is Faraday's law, and it is why a moving magnet lights a bulb. That link runs through flux rather than through the fields directly, and it is worked in Topic 12.4. A light wave is an electric field and a magnetic field sustaining each other, which is Topic 14.4. And EK 12.2.B.4 covers the Hall effect, where a magnetic field acting on moving charges in a conductor produces a potential difference across it, an electric consequence of a magnetic cause.

On the exam, electric fields are Topic 10.3 inside Unit 10, weighted at 15 to 18 percent of the multiple-choice section. Magnetic fields are Topic 12.1 and their action on moving charge is Topic 12.2, inside Unit 12 at 12 to 15 percent. In AP Physics C: Electricity and Magnetism the split is wider still: electric fields in Unit 8 at 15 to 25 percent, magnetic fields in Unit 12 at 10 to 20 percent, with the Biot-Savart law and Ampere's law added.

From here, magnetic flux vs magnetic field covers what happens when you push a field through a surface, and electric field vs electric force covers the field-against-force distinction on the electric side alone.