Faraday's Law with Acceleration

[KabooHahahein]

I decided to join this forum because we were baffled on the following fact made by a professor. We were hoping to get this cleared up here, since the prof said the math was complicated.

Let's assume any arbitrary circuit (forming an area) moving at velocity v through a perpendicular field B to the plane of the area of the circuit. Now, the change in magnetic flux is 0 in constant v. However, it was pointed out that it is not 0 in any acceleration.

Our prof pointed out that it can be imagined as an increasing area as a magnetic lawnmower increases in speed.

How are the mathematics applied to this sort of problem?

Thank you!

 

[y33t]

This is not the section to ask help for homeworks or assignments but I'll give you a go for this time. Please use the dedicated section for these kinds of purposes from now on.

You need to be more specific ;

Is the circuit is completed ?
Are there any currents flowing in the circuit ?
If so what are the specs ?

It has nothing to do with the area of the pcb or the circuitary. Your professor probably asked for this ;

Even if there is no current flow in the circuit, due to electrons in the pcb traces and the wiring, when the whole system accelerates you will be accelerating the electrons with the system. A moving charge will induce an electric field and a time varying electric field will induce a magnetic field . Taking derivative of velocity will give you acceleration and taking curl of electric field will give you minus derivative of magnetic field. From now on it's convenient to express ;

F = q.v x B

q is the coulomb of your charge, v is velocity and B is magnetic flux density vector.

Although this might not be the case at all, depending on what you really mean.

 

[KabooHahahein]

The circuit is completed, and we're talking about the induced EMF (resulting in an induced current) from Faraday's Law from a change in flux. Initially, I would assume that there are no currents on the circuit.

Now our issue is that the flux is (B)(A), and that it is constant under an externally generated constant magnetic field. Shouldn't the change in flux be 0, no matter whether the circuit is at constant velocity or acceleration through this constant field?

I apologize for making this look like homework. This is not anything assigned, we were simply curious as how it's possible that under a changing velocity, the change in magnetic flux through the loop would not be zero.

 

[y33t]

The circuit is completed, and we're talking about the induced EMF (resulting in an induced current) from Faraday's Law from a change in flux. Initially, I would assume that there are no currents on the circuit.

Now our issue is that the flux is (B)(A), and that it is constant under an externally generated constant magnetic field. Shouldn't the change in flux be 0, no matter whether the circuit is at constant velocity or acceleration through this constant field?

I apologize for making this look like homework. This is not anything assigned, we were simply curious as how it's possible that under a changing velocity, the change in magnetic flux through the loop would not be zero.

If flux (B) is constant you have a time-independent electric field also implying there is DC operation going on in the circuit.

There is no such thing as (B)(A).

$\int$$\int$ (dB / dt) ds = $\oint$ ($\nabla$x E) ds

 

[sardar]

Hello and welcome to the forum! It's great that you are seeking clarification on this topic. Faraday's law states that a changing magnetic field will induce an electromotive force (EMF) in a conductor. This means that when a conductor, such as a circuit, moves through a magnetic field, the changing magnetic flux will generate an EMF. This EMF can then cause a current to flow in the circuit.

In the scenario you described, the circuit is moving at a constant velocity, so there is no change in the magnetic flux and therefore no induced EMF. However, when the circuit is accelerating, the magnetic flux is changing and therefore an EMF is induced.

The mathematics for this problem involve calculating the rate of change of the magnetic flux, which is given by the equation dΦ/dt, where Φ is the magnetic flux and t is time. This rate of change will depend on the velocity and acceleration of the circuit, as well as the strength of the magnetic field.

To better understand this concept, you can think of the circuit as a loop of wire moving through the magnetic field. As the loop moves, it cuts through the lines of magnetic flux, which causes a change in the magnetic flux and therefore an induced EMF. The faster the loop moves, the more lines of flux it cuts through and the greater the induced EMF.

I hope this helps to clarify the concept for you. If you have any further questions, please don't hesitate to ask. Happy experimenting!