# Electromagnetic induction (finding ΔΦ).

• KarlsShwarzschild
In summary, the conversation discusses the relationship between time and electromagnetic force (EMF) inside a coil while a magnet is inside it. The formula used is ##\mathcal E = -N \frac{\Delta \Phi}{d}\sqrt{2gh}##, which represents the average EMF while the magnet is inside the coil. However, this average is actually zero due to symmetry and the fact that the magnet continues to accelerate inside the coil, resulting in an uneven graph of ##\mathcal{E}## vs ##t## with a total integral of 0.
KarlsShwarzschild

I am unsure if I understand what you are doing. It seems ##\frac{d}{\sqrt{2gh}}## is approximately the time that the magnet spends inside the coil. You are also using $$\mathcal{E} = -N\frac{d\Phi}{dt}$$I suppose the average rate of change of flux in a time ##\Delta t## is ##\frac{\Delta \Phi}{\Delta t}##, from which it follows that the average EMF ##\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}##. So your construction ##\mathcal E = -N \frac{\Delta \Phi}{d}\sqrt{2gh}## is the time-averaged EMF inside the coil whilst the magnet is inside the coil. However this is zero, because ##\frac{1}{T} \int_0^T -N\frac{d\Phi}{dt} dt = 0##, since the flux linked in the coil is the same when the magnet is at the top of the coil as when it leaves (I assume necessary symmetry here ).

Plus, the magnet actually still accelerates inside the coil, so a graph of ##\mathcal{E}## vs ##t## has an uneven shape (but still a total integral of 0).

berkeman
KarlsShwarzschild said:
I'm not too sure if I overestimated the prefix, guess we'll find out

rude man and berkeman

## 1. What is electromagnetic induction?

Electromagnetic induction is the process of creating an electric current in a conductor by changing the magnetic field around it.

## 2. How does electromagnetic induction work?

When a conductor, such as a wire, is moved through a magnetic field or when the magnetic field around a conductor is changed, it creates a flow of electrons, which results in an electric current.

## 3. What is the equation for finding ΔΦ in electromagnetic induction?

The equation for finding ΔΦ, or change in magnetic flux, is ΔΦ = B x A x cos(θ), where B is the magnetic field strength, A is the area of the conductor, and θ is the angle between the magnetic field and the normal to the area of the conductor.

## 4. What is the significance of ΔΦ in electromagnetic induction?

ΔΦ is a measure of the change in magnetic flux, which is essential in determining the amount of induced current in a conductor. It is also used to calculate the magnitude and direction of the induced emf (electromotive force).

## 5. What are some practical applications of electromagnetic induction?

Electromagnetic induction has many practical applications, including generators, motors, transformers, and induction cooktops. It is also used in wireless charging, electromagnetic braking systems, and metal detectors.

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