# Is there any theoretical reason behind multiplying by N when using F's law of induction?

1. Nov 11, 2014

### 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 dont 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.

Last edited: Nov 11, 2014
2. Nov 15, 2014

### Staff: Mentor

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

3. Nov 16, 2014

### Staff: Mentor

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.

4. Nov 16, 2014

### davidbenari

jtbell:

I guess you have answered my Q. thanks.