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IN A SIMPLE CIRCUIT, WHERE DOES THEENERGY FLOW?

A Collection of Diagrams William Beaty

Electronics students commonly assume that electrical energy flows inside metal wires. Physicsstudents know differently! Normally the electrical energy doesn't flow inside of metals. In fact, theelectrical energy being sent out by batteries and generators is located in empty space: it takes theform of electromagnetic fields surrounding the wires. The diagrams below will show us the details.

While coils will store energy as a magnetic field outside the windings, and while capacitors will storeenergy as an electric field in the insulating layer between the metal plates, an electric circuit handlesenergy a bit differently. An electric circuit as a whole does both at once: it's both coil and capacitor.The energy which flows across a circuit is not moving through the interior of the metal wires. Insteadit flows through the space surrounding the metal parts of the circuit. For example, whenever abattery powers a light bulb, the battery spews electrical energy into space! The electrical energy is

then grabbed firmly by the wires and guided by them. The energy flows parallel to the wires, andeventually it dives into the light bulb filament. There it drives the metal's charges against theresisting force of electrical "friction," and the electrical energy gets converted into thermal energy. Anelectric circuit is like a duct for electrical energy, but this duct has no walls.

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Fig. 1 A SIMPLE CIRCUIT A battery is connected to a resistor such as a light bulb. The batteryconverts its chemical fuel into waste products, and the resistor gets hot.

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Fig. 2 THE CONDUCTIVE PATH: CURRENT  All conductive materials contain movable charges. The resistor and

the battery's electrolyte both are conductive. When we include themwith the wires, we can see that an electric circuit is a complete circlewhich is full of "fluid" charge. It acts like a liquid flywheel; a flywheelhidden inside a closed ring of pipe.

Fig. 3 THE MAGNETIC FIELD CAUSED BY THE CURRENTLOOP

 A circular electric current is an electromagnet. The magnetic field-lines

form rings around the conductors. Note that I've slightly tilted the circlesto make them visible. In reality, we should be looking at them edge-on.(Also: note that the physics name for the magnetic field is "B-field".)

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Fig. 3A THE MAGNETIC FIELD CAUSED BY THE CURRENTLOOP

Here's a better view of the above circuit... the three-dimensionaloblique view.

To be more accurate, we need to draw more than just two patterns.

Between the two patterns above, draw a third. Then between each of those draw more and more. The end result looks like "tubes" of magnetic flux surrounding the wires.

Fig. 4 TWO CHARGED CONDUCTORS: VOLTAGE Everything connected to one battery terminal acquires the sameelectrical potential (voltage.) The circuit acts like two separate

conductors, one with a positive charge imbalance and one withnegative.

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Fig. 5 THE ELECTRIC FIELD CAUSED BY THE OPPOSITE

CHARGES 

The two charged wires act like the plates of a capacitor. "Force lines"of e-field spew out of one charged conductor and dive into the other.This is a side view of the e-field in the plane of the circuit. In a full 3-Dview we'd see the lines spreading outwards in radial star-shapes from

each wire.

Fig. 5A THE ELECTRIC FIELD CAUSED BY THE OPPOSITECHARGES 

 Again, here's a 3D oblique view. The two halves of the circuit act as

opposite-charged wires with e-field flux connecting them. As withfigure 3A we need to draw a third pattern between the two above, thendraw more between those until the whole wire is covered with bentsheets of electrostatic flux which arcs between the wires.

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Fig. 6 E-FIELD AND B-FIELD TOGETHER

Fig. 6A E-FIELD AND B-FIELD TOGETHER

The 3D oblique view of the two fields. Add more and more patternsbetween the two shown above, until empty space is packed full of "hair." Note that most of the flowing energy lies between the twowires... but quite a bit also surrounds the "cable pair" as a whole. Also

note that the E and B flux lines are always at 90 degrees to each other.When we say that E and B in light waves are always perpendicular, theabove diagram shows what such a thing looks like.

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Fig. 7 THE ENERGY FLOW (POYNTING FIELD)

Electromagnetic energy flows out of the battery and into the empty

space around the circuit. It flows parallel to the connecting wires, then itdives into the resistor. The field of energy flow is found by multiplyingthe e-field by the b-field (E x B vector cross-product.)

Fig. 8 ENERGY FLOW FIELD WITH E-FIELD IN GRAY

Note that the energy always flows perpendicular to the lines of e-field

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Fig. 9 ENERGY FLOW WITH B-FIELD IN GRAY

Note that the energy always flows perpendicular to the lines of b-fieldtoo.

Fig. 10 A SIMPLE CIRCUIT?

When all the separate invisible phenomena are displayed together,you can see why "electricity" might be a bit hard to understand. And

this diagram only shows a two-dimensional slice; a sort of side view of the fields. The real fields are 3D and volume-filling, so an accuratedrawing would look like a black glob of hairs.

SEE ALSO:

mit.edu, TEAL animated field diagrams:

Magnetic fieldse-fieldsFaraday induction: dynamic magnetic fieldsEM and wavesGuided tour 

Right-angle circuitry (bill b)'Electricity' is not energy (bill b)Bulb w/Lightswitch xmission line anim.Understanding Electricity and Circuits: What the Text Books Don't Tell You (pdf)Unifying electrostatics and electric circuits Chabay & Sherwood 1999 (.PDF) ,(arcv)Roy McCammon's GIFs of electric and magnetic fields in EM waves:http://www.armory.com/~rstevew/Public/Tutor/RoyMcC_Waves/index.html

How can longwave EM pass through tiny holes? (bill b)

Poynting-flow diagrams are *extremely* rare in physics texts, and the majority of physicsinstructors seem unaware that they exist. Perhaps the reason is that, as children, allphysicists were taught that energy flows *inside* the wires. Childhood sciencemisconceptions are extremely difficult to cure. They frequently remain unexamined, and oftenpersist well into adulthood. For example, Feynman mentions the Poynting-flow concept in"The Feynman Lectures," Chapter 27, and performs EM-field energy flow analysis oncapacitors and resistors, but he doesn't analyze 2-wire transmission lines, nor does he linkthe components together into a continuous system as with my figure 7 above. Worse, at onepoint he bad-mouths the whole concept, and asserts that we should not change our originalviewpoint, but instead suggests that we continue to assume that the energy flows inside the

copper! Feynman? Counsiling dishonesty rather than harnessing this "alternate toolkit?" Amazing. (And ...doesn't he know that the speed of light inside solid copper, the speed whichcauses Skin Effect phenomena, is down in the meters per second range?) If themisconception that "energy flows inside wires" had such a deleterious effect on an honestfree-thinker like Feynman, think how much trouble any more conventional minds would havewith it.

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Here's another version of my figure 7: page 417, Fig 10-19, found in:

ELECTROMAGNETICS 2nd Ed., John D. Kraus & Keither R. Carver, McGraw-Hill1973

This is interesting, because it shows one place where poynting vector energy flow is acrucial idea: Antenna Design! Kraus Electromagnetics is essentially an antenna design bookaimed at physics students.

http://amasci.com/elect/poynt/poynt.html 

Created and maintained by Bill Beaty . Mail me at: .

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