Imagine a gigantic circuit with wires so long that they stretch for light-seconds, connecting a battery, a switch, and a light bulb just one meter away. The big question is: how long does it take for the light bulb to turn on after you close the switch? Initially, I thought it would take 1/c seconds, where c is the speed of light. This sparked a lot of debate and confusion, so let’s clear up some misconceptions about how electric circuits work.
Many people were concerned that my answer suggested we could communicate faster than the speed of light, which would break the rules of causality. This reaction showed a common misunderstanding of electric circuits. To explore this, I built a smaller version of the circuit, 10 meters long, to see how quickly the light bulb would light up after closing the switch.
One common misconception is that electrons carry energy directly from the battery to the light bulb. While electrons do move through the circuit, they don’t transport energy in the way you might think. Instead, energy is transferred through an electric field established in the wire.
When a circuit is powered, electrons in the wire are accelerated by this electric field, which is created by the battery and the surface charges on the wires. The actual speed of electrons is quite slow, with an average drift velocity of less than 0.1 millimeters per second. However, the electric field propagates at the speed of light, allowing for almost instantaneous energy transfer across the circuit.
Another misconception is that mobile electrons push each other through the circuit. In reality, the charge density inside a conductor averages to zero, meaning that the forces between electrons and the positive atomic cores cancel out. The electric field, which is responsible for moving electrons, is established by the battery and the surface charges on the wires.
When the switch is closed, the surface charges on either side of the switch neutralize each other, creating a new electric field that propagates outward at the speed of light. This change in the electric field is what causes the current to flow through the load, such as a light bulb.
To validate these concepts, I worked with Richard Abbott from LIGO to measure the voltage across a resistor in our scaled-down circuit. When we applied a pulse, we observed that the voltage across the resistor rose to about four volts within a few nanoseconds. This showed that a significant amount of power was being transferred, much more than what would be expected from just leakage current.
The electric field in the wire is influenced not only by the battery but also by the surface charges that develop along the wire. These surface charges create a gradient that facilitates the movement of electrons, allowing for the rapid establishment of the electric field necessary for current flow.
Some viewers were worried that my original claim violated causality, suggesting that the light bulb would only illuminate if the circuit were complete. However, I should have clarified that the bulb lights up regardless of whether the circuit is fully connected. The electric field can induce current in the load even if the circuit is not entirely closed.
To further illustrate these principles, Ben Watson created simulations using Ansys software to visualize the electric field dynamics in the circuit. These simulations showed that the electric field radiates outwards when the switch is closed, generating current in the load almost immediately.
In summary, the key takeaway is that electrons do not carry energy from the battery to the bulb; instead, they are pushed along by an electric field created by surface charges and the battery itself. This understanding shifts the focus from individual electrons to the electric fields that govern their movement.
The discussion surrounding my initial video has sparked a wealth of responses and further exploration into the nature of electric circuits. I appreciate the engagement and insights from the electrical engineering community, which have enriched our understanding of these concepts.
For those interested in delving deeper into electricity and magnetism, I recommend exploring educational resources that emphasize the role of fields in circuits, as this perspective can illuminate many previously misunderstood aspects of electrical engineering.
Gather materials such as a battery, wires, a switch, and a light bulb. Construct a simple circuit and observe how the light bulb reacts when the switch is closed. Pay attention to the time it takes for the bulb to light up and discuss how the electric field facilitates this process.
Use a simulation tool like Ansys or a similar software to visualize how the electric field propagates in a circuit when the switch is closed. Analyze the simulation to understand the role of surface charges and how they contribute to the rapid establishment of the electric field.
Calculate the drift velocity of electrons in a copper wire using the formula $$v_d = frac{I}{n cdot A cdot e}$$, where $I$ is the current, $n$ is the number of charge carriers per unit volume, $A$ is the cross-sectional area, and $e$ is the charge of an electron. Discuss why this velocity is much slower than the speed of light.
Conduct an experiment to measure the voltage across different points in a circuit. Use these measurements to infer the distribution of surface charges along the wire and discuss how these charges influence the electric field and current flow.
Engage in a debate about the concept of causality in electric circuits. Discuss whether the light bulb can illuminate without a fully closed circuit and how the electric field can induce current in the load. Use evidence from experiments and simulations to support your arguments.
Electricity – The set of physical phenomena associated with the presence and motion of electric charge – Electricity is essential for powering our homes and devices, and it is generated by the movement of electrons through a conductor.
Circuits – A closed loop or pathway that allows electric current to flow – In physics class, we learned how to design circuits to control the flow of electricity using resistors and capacitors.
Electrons – Subatomic particles with a negative charge that orbit the nucleus of an atom – Electrons play a crucial role in electricity as their movement through a conductor constitutes an electric current.
Energy – The capacity to do work, which in the context of electricity, is often measured in joules – The energy consumed by an electrical appliance is calculated by multiplying the power rating by the time it is used, expressed as $E = P times t$.
Field – A region in which a force is exerted on a charged particle, often described by electric field lines – The strength of an electric field $E$ is defined as the force $F$ per unit charge $q$, given by $E = frac{F}{q}$.
Current – The flow of electric charge, typically measured in amperes (A) – Ohm’s Law states that the current $I$ through a conductor between two points is directly proportional to the voltage $V$ across the two points, expressed as $I = frac{V}{R}$.
Voltage – The electric potential difference between two points, measured in volts (V) – A battery provides a voltage that pushes electrons through a circuit, enabling devices to function.
Charges – Physical properties of particles that cause them to experience a force within an electric field – Like charges repel each other, while opposite charges attract, as described by Coulomb’s law: $F = k frac{|q_1 q_2|}{r^2}$.
Battery – A device consisting of one or more electrochemical cells that convert stored chemical energy into electrical energy – The battery in a smartphone provides the necessary voltage to power the device when it is not connected to an external power source.
Resistance – A measure of the opposition to the flow of electric current, typically measured in ohms (Ω) – The resistance of a wire increases with its length and decreases with its cross-sectional area, as described by the formula $R = rho frac{L}{A}$, where $rho$ is the resistivity.
