# Looking for a formula for calculating maximum induced AC voltage in two air coils next to each other

I've got a question about electromagnetic induction. I've already done some research but I'm unable to find the easy solution.

I want to calculate somehow maximum voltage peak that will be induced in secondary coil in AC circuit. For sure I have all input data here.

Circuit is obvious. There's primary air coil L1 connected trough a resistor R to sinewave AC voltage source U1 (oscillating with frequency f). Through the L1 coil flows AC current I.

I know every value here including L1 inductance, diameter, turns qty, winding wire radius and even non-ideal solenoid params like resistance and capacitance.

Next to the coil L1 there's secondary air coil L2, also with all known parameteres, and L2 is located next to L1 the distance l (in a straight line). L2 is contected to analog voltage meter to measure U2 voltage peaks.

Electric circuit: Coils phisical relation: Question: How to calculate maximum voltage peak U2 that will be induced in the L2 coil? Does a simple, school formula U2max = ... even exists? Even poor approximation would be good enough.

• For two coils L1, and L2 that are magnetically coupled, there exists a coefficient of mutual induction. For coil 1: U1 = L1di1/dt + M di2/dt. For coil L2: U2=L2 di2/dt + Mdi1/dt. Determining the magnitude of this M is another matter altogether. – Bart Aug 18 '17 at 8:36
• This link may help you to get a better understanding of coupled inductors: electronics-tutorials.ws/inductor/mutual-inductance.html – Bart Aug 18 '17 at 8:41

There is no simple formula for Mutual Coupling.

But there are many books on the subject.