Understanding Faraday's Law with Solenoids

[davidbenari]

It is a well known fact that whenever we want to calculate the emf in a solenoid we usually multiply the changing flux for one loop times N, which is the number of turns in the solenoid.

But why is this?

For example, in the case of amperes law, I know that it makes sense to add currents because you are considering the line integral, one can think of it like

$\oint \mathbf{B} \cdot \mathbf{dl} = \oint (\mathbf{\sum_i B_i}) \cdot \mathbf{dl} = \sum_i ( \oint \mathbf{B} \cdot \mathbf{dl} ) _ i = \sum_i \mu_0 I = \mu_0 \sum_i I_i$

In that case, currents clearly should add, but I don't see why currents or turns in the solenoid are added in any "deep" sense (when applying Faraday's law).

Thanks and sorry if my question is unclear.

 

[Evo]

It is a well known fact that whenever we want to calculate the emf in a solenoid we usually multiply the changing flux for one loop times N, which is the number of turns in the solenoid.

But why is this?

For example, in the case of amperes law, I know that it makes sense to add currents because you are considering the line integral, one can think of it like

$\oint \mathbf{B} \cdot \mathbf{dl} = \oint (\mathbf{\sum_i B_i}) \cdot \mathbf{dl} = \sum_i ( \oint \mathbf{B} \cdot \mathbf{dl} ) _ i = \sum_i \mu_0 I = \mu_0 \sum_i I_i$

In that case, currents clearly should add, but I don't see why currents or turns in the solenoid are added in any "deep" sense (when applying Faraday's law).

Thanks and sorry if my question is unclear.

Is there anything you can do to condense this or make it clearer?

 

[jtbell]

It is a well known fact that whenever we want to calculate the emf in a solenoid we usually multiply the changing flux for one loop times N, which is the number of turns in the solenoid.

But why is this?

Gah, I can't believe nobody tackled this, including me.

Suppose you have a single loop that produces (for a given changing-magnetic-field configuration) an emf of 1.5 volts. Now suppose you have a coil or solenoid containing, say, 5 of these loops (turns). The loops are electrically in series, so you have 5 emf's in series, 1.5 volts each. It's like having 5 (ideal) dry-cell batteries in series, each with an emf of 1.5 volts, producing a total emf of 7.5 volts.

 

[davidbenari]

jtbell:

I guess you have answered my Q. thanks.

 

[sardar]

First of all, it is important to understand that Faraday's law is based on the principle of electromagnetic induction, which states that a changing magnetic field will induce an electric field. In the case of a solenoid, the changing magnetic field is caused by the changing current flowing through the loops of the solenoid. This changing magnetic field then induces an electric field within the solenoid.

Now, to understand why we multiply the changing flux by the number of turns in the solenoid, we need to look at the definition of flux. Flux is the amount of a vector field (in this case, the magnetic field) passing through a given area. In the case of a solenoid, the magnetic field is confined within the loops of the solenoid. Therefore, the amount of flux passing through one loop is directly proportional to the number of turns in the solenoid. This is because each turn of the solenoid contributes to the overall magnetic field within the solenoid.

So, when we multiply the changing flux by the number of turns in the solenoid, we are essentially taking into account the contribution of each turn to the overall magnetic field and the resulting induced electric field. This is why it is necessary to consider the number of turns in a solenoid when applying Faraday's law.

In summary, the reason for multiplying the changing flux by the number of turns in a solenoid is based on the fundamental principles of electromagnetic induction and the definition of flux. It may seem like a simple mathematical operation, but it is rooted in the underlying physical principles of electromagnetism.