If you have ever used an induction cooker, you might have wondered about the science behind it. One curious question is how the electric currents, also known as eddy currents, flow in the induction cooking vessel. In this article, we will explore how to theoretically predict the streamlines of these induced currents and how to measure them.
Theory Behind Electric Current Streamlines in Induction Cooking Vessel
The shape of the induced eddy currents in induction cooking depends on the shape of the fluctuating magnetic field and the shape of the cooking vessel. To theoretically predict the streamlines, we can use Maxwell’s equations, which describe the behavior of electric and magnetic fields. These equations connect the electric and magnetic fields to the sources of these fields, namely, electric charges, electric currents, and changing electric and magnetic fields.
There are two main equations we can use to predict the electric currents in the induction cooking vessel. The first is Faraday’s law of electromagnetic induction, which states that the changing magnetic field induces an electromotive force (EMF) in a conductor. The second is Ohm’s law, which relates the current through a conductor to the voltage across it. Combining these equations, we get the following:
∇ × E = - dB/dt (Faraday's law)
J = σ E (Ohm's law)
where ∇ × E is the curl of the electric field, dB/dt is the rate of change of the magnetic field, J is the current density, σ is the conductivity of the material, and E is the electric field.
These equations can be solved numerically using a computer program like COMSOL Multiphysics, which can simulate the behavior of electric and magnetic fields in real-world systems. The program can model the induction cooking vessel with its varying magnetic field and predict the shape of the eddy currents in the vessel.
Measurement of Electric Current Streamlines in Induction Cooking Vessel
Now that we know how to theoretically predict the streamlines of the electric induced currents in an induction cooking vessel, how can we measure them in real life? One way is to use a technique called magnetic field imaging, which allows us to visualize the magnetic field lines and the resulting eddy currents in the cooking vessel.
One common magnetic field imaging method is called magnetic particle imaging (MPI), which uses superparamagnetic iron oxide nanoparticles as tracers. These nanoparticles are injected into the cooking vessel and are magnetized by the magnetic field. Then, a magnetic field gradient is applied, causing the nanoparticles to move in the direction of the gradient. As the particles move, they generate a magnetic field that is detected by a magnetic sensor outside the vessel. By analyzing the magnetic field signal, we can reconstruct the shape of the induced eddy currents.
Eddy Current Loops
A question often asked about eddy currents is whether they have to be closed or not. The answer is that all current must form a loop, which means that the eddy currents are closed. The diagram might seem to show some lines that are not closed, but it is only because the image is cropped. The magnetic field lines either extend to infinity or form a loop. For instance, a perfect bar magnet has two lines normal to the N and S poles that extend to infinity, but they seem open because the image is cut off.
Conclusion
The electric induced currents, or eddy currents, in an induction cooking vessel have a complex shape that depends on the magnetic field and the vessel’s shape. Using Maxwell’s equations, we can theoretically predict the streamlines of these currents and numerically solve them using a computer program like COMSOL Multiphysics. We can also measure the shape of the currents experimentally using a magnetic field imaging technique like magnetic particle imaging. Finally, we note that all current must form a loop, which means that the eddy currents are closed, despite how this might appear in diagrams.
Electric Current Streamlines In Induction Cooking Vessel
If you have ever used an induction cooker, you might have wondered about the science behind it. One curious question is how the electric currents, also known as eddy currents, flow in the induction cooking vessel. In this article, we will explore how to theoretically predict the streamlines of these induced currents and how to measure them.
Theory Behind Electric Current Streamlines in Induction Cooking Vessel
The shape of the induced eddy currents in induction cooking depends on the shape of the fluctuating magnetic field and the shape of the cooking vessel. To theoretically predict the streamlines, we can use Maxwell’s equations, which describe the behavior of electric and magnetic fields. These equations connect the electric and magnetic fields to the sources of these fields, namely, electric charges, electric currents, and changing electric and magnetic fields.
There are two main equations we can use to predict the electric currents in the induction cooking vessel. The first is Faraday’s law of electromagnetic induction, which states that the changing magnetic field induces an electromotive force (EMF) in a conductor. The second is Ohm’s law, which relates the current through a conductor to the voltage across it. Combining these equations, we get the following:
where ∇ × E is the curl of the electric field, dB/dt is the rate of change of the magnetic field, J is the current density, σ is the conductivity of the material, and E is the electric field.
These equations can be solved numerically using a computer program like COMSOL Multiphysics, which can simulate the behavior of electric and magnetic fields in real-world systems. The program can model the induction cooking vessel with its varying magnetic field and predict the shape of the eddy currents in the vessel.
Measurement of Electric Current Streamlines in Induction Cooking Vessel
Now that we know how to theoretically predict the streamlines of the electric induced currents in an induction cooking vessel, how can we measure them in real life? One way is to use a technique called magnetic field imaging, which allows us to visualize the magnetic field lines and the resulting eddy currents in the cooking vessel.
One common magnetic field imaging method is called magnetic particle imaging (MPI), which uses superparamagnetic iron oxide nanoparticles as tracers. These nanoparticles are injected into the cooking vessel and are magnetized by the magnetic field. Then, a magnetic field gradient is applied, causing the nanoparticles to move in the direction of the gradient. As the particles move, they generate a magnetic field that is detected by a magnetic sensor outside the vessel. By analyzing the magnetic field signal, we can reconstruct the shape of the induced eddy currents.
Eddy Current Loops
A question often asked about eddy currents is whether they have to be closed or not. The answer is that all current must form a loop, which means that the eddy currents are closed. The diagram might seem to show some lines that are not closed, but it is only because the image is cropped. The magnetic field lines either extend to infinity or form a loop. For instance, a perfect bar magnet has two lines normal to the N and S poles that extend to infinity, but they seem open because the image is cut off.
Conclusion
The electric induced currents, or eddy currents, in an induction cooking vessel have a complex shape that depends on the magnetic field and the vessel’s shape. Using Maxwell’s equations, we can theoretically predict the streamlines of these currents and numerically solve them using a computer program like COMSOL Multiphysics. We can also measure the shape of the currents experimentally using a magnetic field imaging technique like magnetic particle imaging. Finally, we note that all current must form a loop, which means that the eddy currents are closed, despite how this might appear in diagrams.